text:
Shaarey Tzaddik, Vol. 2
By Rabbi Gedaliah Aharon Kenig, zatzal
Excerpt from Letter 54
Translated by Dovid Sears
L'ilui nishmas Shlomo ben Binyamin Ze'ev Cheshin, zal
At the time when opposition [toward the early Breslever Chasidim] was raging, and the dreadful persecutions of our master, Reb Noson, may his merits shield us, and his righteous followers, reached their peak, many [Breslever chasidim] complained and wept before Reb Noson, because what they were going through was beyond endurance. They begged him: "Our master and teacher! We know that it is surely within your holy power to do something so that our adversaries will receive the heavenly punishment that is coming to them. Why does our master remain silent, while the holy is devoured [by the unholy], G-d forbid? Please do whatever you can with your holy power, and put an end to the strife against you and against us!"
Our master Reb Noson replied, "Listen to me, my children and my disciples, and know, my friends: it is not our way to afflict anyone, whoever he may be! This is not [the path] we received from our holy Rebbe [Rabbi Nachman], may his merits shield us. Rather, this is what we received from him: to conquer the whole world through prayer, and Hashem will do what is good in His sight.
"On the contrary, we need to exert ourselves with the greatest effort to create sanctified vessels that can contain holiness and wisdom for the sake of our adversaries and opponents, as well. We must concern ourselves with them, so that in the end, they too will come to their proper tikkun (healing of the soul). For they are our fellow Jews, [who are called] 'holy seed,' a 'beloved nation,' a 'nation faithful to G-d,' children of those He has tested, children of Abraham, Isaac and Jacob."
Even if this [conflict] has persisted for so long, due to the power of free choice, which has cast aside and uprooted so many from their proper places, which is the cause of all our hardships and sufferings and persecutions, and the confusions that threaten to disturb our relationship to Hashem, G-d forbid—we will not lose our strong faith and hope, with the help of Hashem. We have no recourse but to the words of our forefathers and holy rabbis, who urged us to raise our eyes above always, and to supplicate constantly before Hashem, that He have mercy upon on his people Israel, a holy nation, and pray and pray again. As it is written, "Hope unto Hashem (kavei el Hashem)…" and go back again and hope, [as the verse continues, "…be resolute and strengthen your heart, and hope unto Hashem" (Psalms 27:14)], as our Sages state (Rabbi Chama son of Rabbi Chanina in Berakhos 32b), and as we received from our master, King Chizkiyahu, peace be upon him.
King Chizkiyahu declared that he possessed a tradition from his ancestor King David that "even is a sharp sword is against one's neck, he should not desist from praying for mercy," Berakhos 10a.).
[We must persist] until Hashem's mercy prevails upon us and upon all Israel, "and again you pity us and suppress our transgressions, and according to the days You afflicted us, you cause us to rejoice," speedily in our days, amen!
From "Breslov Eikh she-Hu: Customs and Good Practices" compiled by Dovid Zeitlin and Dovid Sears
Khof Sivan
It was customary throughout the Ukraine and Russia to recite selichos on the twentieth of Sivan, including in the Breslover community. This commemoration of the 6,000 martyrs of the Nemirov massacre of 1648 persisted in Eretz Yisrael and chutz la-aretz until recent years, when it began to fall into neglect. However, Reb Noson mentions it in Likutey Halakhos.
(See Likutey Halakhos, Shluchin 5:36; Chovel Be-chavero 3:7, 9. The selichos for Khof Sivan are printed in the Siddur Tefillah Yesharah-Berditchev and elsewhere.)
Reb Avraham Sternhartz used to fast on Khof Sivan.
(Rabbi Avraham Shimon Burshteyn, in the name of Rabbi Moshe Burshteyn)
Ches Tammuz
In Uman, selichos were also recited on the eighth of Tammuz, when many thousands of Jewish men, women, and children were slaughtered during the Haidamak uprisings of the same period. However, this minhag has also fallen into disuse.
Reb Avraham Sternhartz used to fast on Ches Tammuz.
Khof-Beis Tammuz
The yahrtzeit of Rabbi Levi Yitzchok Bender, the central figure in the Breslov Kehillah of Yerushalayim after WWII, is 22 Tammuz. For a brief biography of Reb Levi Yitzchok, see here. A rare video of one of his shmuessen in Yiddish is also available online here. Together with his lifelong friend, Reb Elyah Chaim Rosen, Reb Levi Yitzchok rebuilt the Breslov community and devoted himself to preserving and passing on the Breslov mesorah from Uman. Much of this material has been transcribed from audio tapes and published as "Siach Sarfey Kodesh" in eight volumes.
Khof-Gimmel Tammuz
This is the yahrtzeit of Rabbi Gedaliah Aharon Kenig, talmid muvhak of Rabbi Avraham Sternhartz and founder of Mosdos Nachal Novea Mekor Chochma, the umbrella organization of the Tsfat Breslov community. Reb Gedaliah was a reknowned for his ahavas Yisrael, arichas apayim, and great wisdom both in understanding people and in all areas of Torah, particularly pnimiyus ha-Torah. He edited and published several seforim written by other Breslover Chassidim, including his teacher Reb Avraham's Tovos Zikhronos and Reb Ephraim ben Naftali's Likutey Even / Tefillas ha-Boker, as well as one original work, Chayei Nefesh, on the nature and role of the tzaddik. His other writings remain in manuscript.
Khof-Gimel Tammuz is also the yahrtzeit of sixteenth century kabbalist Rabbi Moshe Cordovero of Tzefas, author of Pardes Rimonim, Tomer Devorah, Ohr Ne'erav, and other important mystical works—a tzaddik with whom Reb Gedaliah felt a deep lifelong affinity. Reb Elazar, his brothers, and other chaveirim usually visit Reb Gedaliah's kever on Har ha-Zeisim in Yerushalayim on the yahrtzeit, where they recite Tehillim and pray for Klal Yisrael in his merit.
An English translation of the first half of Reb Gedaliah's "Chayei Nefesh" is available on the sidebar of this website. It is hoped that his other works, which include original commentaries on Likutey Moharan and Tikuney Zohar, as well as his letters and an encyclopedia of terms in Rebbe Nachman's writings, will be published in the near future, be-ezras Hashem.
JCC Manhattan: Rebbe Nachman and You: Contemplative Writing From the Soul
Chaya Rivka Zwolinski
Returning for an extended workshop with all-new material: Are you a curious blogger or journal writer, a beginner or published author, or just interested in getting to know more about yourself? Have you ever wanted to write from a deeper place inside you? Nourished by the hidden wellsprings of ancient Jewish wisdom, Rebbe Nachman's stories are enchanting, dramatic, at times even amusing. But most of all they are elixirs that reveal and heal the soul. In this four-part workshop, we'll take key concepts from these stories for writing prompts, and then write in your choice of several genres, such as narrative essay or memoir, poetry, lists, expository essay or free-form journaling, and more. Share and discuss. Be inspired and discover new aspects of self.
See here for more information.
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From Breslov Eikh Shehu: Breslov Customs and Practices, Past and Present, compiled by Dovid Zeitlin and Dovid Sears (in-progress)
Shavuos Customs
Shavuos was one of the three fixed times of the year when Breslover Chassidim came to the Rebbe. Therefore, in recent years it has become common for many Breslovers travel to Uman to spend Shavuos near the Rebbe's tziyun. (However, there is no requirement to do so; the only time a Breslover Chassid is obligated to travel to Uman is for Rosh Hashanah.)
However, in Reb Noson's day, his talmidim used to travel to him for Shavuos. They would try to arrive in time to conclude the counting of sefiras ha-omer together on the night of Erev Shavuos. One such occasion was Shavuos of 1834, when some eighty followers came to Reb Noson in Breslov. They prayed with such fervor that ever since, Breslover Chassidim refer to this as "der groiser Shavuos."
(See Rabbi Chaim Kramer, "Through Fire and Water," chap. 33, pp. 366-377)
Rabbi Levi Yitzchak Bender mentioned that during Reb Noson's time, when the Breslover Chassidim who had come from far and wide counted the sefirah together on the night before Shavuos, virtually the whole city used to come to witness their fervor. This was an annual event that everyone looked forward to.
(Heard from Rabbi Avraham Moshe Wasilski)
In the Tzefas community, most Breslover Chassidim wear a white caftan on Shavuos at night and during Shacharis-Musaf. However, they do not wear this caftan for Minchah.
(Heard from Rabbi Yitzchok Kenig)
In Tzefas, the Breslov shul is decorated with greenery, following the common minhag.
(Heard from Rabi Yitzchok Kenig. See RaMaH on Orach Chaim 494:3.)
The Steipler Gaon mentioned that in the Ukraine it was customary to spread grass and small twigs on the entire floor of the shul.
(Orchos Rabbenu, vol. II, Bnei Brak 1992, p. 99, sec. 7)
Reb Noson darshans on the minhag of eating dairy foods on Shavuos.
(See Likutey Halakhos, Birkhos ha-Torah 1; Masa U-Matan 4:6; Eruvei Techumin 5:13; Shavu'os 1:4, 2:2; Devarim ha-Yotziyim Min ha-Chai 2:2 and 7; Simanei Behemah ve-Chayah Tehorah 4:40, 46; Mezuzah 2:4)
In Tzefas, as in most communities, the minhag is to eat milchigs after davenning Shacharis, during the Kiddush. However, the day meal is fleishig.
(Heard from Rabbi Yitzchak Kenig. See Shulchan Arukh, Orach Chaim 494:3, with Mishnah Berurah; Likutey MaHaRiCH Vol. III, p. 577.)
Breslover Chassidim traditionally remain awake all night and recite the Tikkun Leyl Shavuos of the Arizal. In the Tzefas community, the chaburah recites the Tikkun together, and the Chassidim recite Kaddish and dance after concluding each section: Chumash, TaNaKH, Mishnayos, etc.
(See Rabbi Chaim Vital, Pri Eytz Chaim, Sha'ar Chag HaShavuos, chap. 1; ; Kitzur SheLaH Masechtas Shavuos: Seder Leyl Shavuos.)
Reb Noson states that the main parts of Tikkun Leyl Shavuos are TaNaKh and Mishnayos. Although the Arizal omits the Mishnayos, the Shelah ha-Kadosh includes them.
(Likutey Halakhos, Kriyas ha-Torah 6:26)
Accordingly, Reb Avraham Sternhartz used to recite the Tikkun Leyl Shavuos with the Mishnayos.
(Heard from Rabbi Nachman Burshteyn)
In a letter to Rabbi Avraham Jacobovitch, Rabbi Shmuel Horowitz writes: "Remaining awake on the night of Shavuos gives life to all of one's conduct for the entire year, both spiritually and physically. One should rejoice, for this is the 'wedding' of Matan Torah -- and one should rededicate himself to the study of the Rebbe's teachings, which are a chiddush niflah, a wondrous innovation that comes from the Future World, from [the Torah of] Atika Setimah [the Hidden Ancient One], destined to be revealed in time to come…"
(Rabbi Shmuel Horowitz, Mikhtevey Shmuel [Jerusalem: Keren Rabbi Yisrael Dov Odesser, first edition], Letter 2, p. 14; cf. Reb Noson's description of the Rebbe's teachings at the beginning of his Hakdamah to Likutey Moharan.)
The Terhovitza Maggid, a close talmid of the Rebbe and a prominent Chassidic leader in his own right, and Reb Menachem Nochum of Chernobyl, author Me'or Einayim, always used to take turns visiting each other to celebrate Shavuos. On Shavuos night, they would dance together in ecstasy all night long. When Reb Nochum grew too old and weak to continue, he sent his son Reb Mordechai of Chernobyl to the Terhovitza Maggid for Shavuos, and they, too, danced all night.
(Rabbi Shmuel Horowitz, Mikhtevey Shmuel [Jerusalem: Keren R' Yisrael Dov Odesser, first edition], Letter 64, p. 201. From this it would seem that the two tzaddikim did not recite the Tikkun Leyl Shavuos.)
Rabbi Shmuel Horowitz states that on Shavuos in Uman, the Chassidim took turns dancing all through the night. Thus, one group was always reciting the Tikkun and another was always dancing.
(Rabbi Shmuel Horowitz, Mikhtevey Shmuel [Jerusalem: Keren R' Yisrael Dov Odesser, first edition], Letter 54, p. 190; ibid. Letter 64, p. 201)
By contrast, Rabbi Levi Yitzchak Bender recalled that the Breslover Chassidim in Uman recited the Tikkun Leyl Shavuos, as is customary, and then danced for a long time. On one occasion, Reb Borukh Getche's danced with the members of his chaburah all night until it was time to get ready for Shacharis.
(Si'ach Sarfei Kodesh V, 303)
Rabbi Nachman Burshteyn heard that in Uman, it was primarily the "ovdim" who danced at such length on Shavuos night. Most of the olam simply recited the Tikkun.
In the Breslov shul in the Katamon section of Yerushalayim, they used to dance after each of the three or four "kaddeishim" during the course of reading the Tikkun.
The melody for "Atah Nigleisa" that we sing on Shavuos night came from the Rebbe Reb Borukh'l of Medzhibuzh, who sang it on Shabbos evening to the words of "Eishes Chayil"—while the melody we sing to "Eishes Chayil," Reb Borukh'l used to sing to "Atah Nigleisa." However, the Rebbe switched them.
Just before alos ha-shachar, it is proper to immerse in the mikveh. Kabbalistically, this mikveh represents the Fiftieth Gate, and is the source of holiness of all immersions in the mikveh throughout the year.
(Likutey Moharan I, 56:7; Rabbi Shmuel Horowitz, Mikhtevey Shmuel [Jerusalem: Keren Rabbi Yisrael Dov Odesser, first edition], Letter 64, p. 201; Rabbi Chaim Vital, Pri Eitz Chaim, Sha'ar Chag HaShavuos, chap. 1)
As mentioned above, Shavuos is one of the five times that the tzibbur davens ki-vasikin.
(Oral Tradition)
Rabbi Levi Yitzchak Bender stated that throughout the Ukraine, including in Breslover communities, it was customary to omit the yotzros on the first day of Shavuos, but to recite them on the second day. In Breslov communities in Eretz Yisrael (where there is only one day of Yom Tov), yotzros are recited during chazoras ha-SHa"TZ on Shavuos.
(See Si'ach Sarfei Kodesh IV, 463)
In America, the Borough Park Breslov congregation does so on both days.
Rabbi Nachman greatly praised the medieval poem "Akdamus Milin" and the regal melody with which it is sung. This remains a highlight of the Shavuos davening in Breslover shuls today. Each stanza is sung by both the chazzan and the congregation, not by alternating stanzas, as in many other communities.
(See Sichos ha-Ran 256)
Reb Avraham used to sing a melody without words prior to Akdamus, and extend and embellish the stanzas with various melodic phrases as he recited them.
Reb Noson mentions the minhag followed by most congregations to recite Sefer Rus on the second day Shavuos (in chutz la'aretz).
(See Likkutei Halakhos, Birkhas ha-Shachar 5:18, 52; Kriyas Shema 5:17; Birkhas ha-Peyros 5:22; et al. This custom is mentioned in Machzor Vitry, based on a midrash in Pesikta Zutra (Midrash Rus); see Likutey Maharich III, p. 579.)
Reb Gedaliah told Reb Aharon Waxler that one should say "shnei se'irim le-khaper" during the Musaf of Shavuos, as in the Musaf of Rosh Hashanah.
(Heard from Rabbi Aharon Waxler. Cf. Siddur Baal ha-Tanya, Musaf shel Shalosh Regalim)
Shavuos is the yahrtzeit of the holy Baal Shem Tov, founder of the Chassidic movement, and the Rebbe's great-grandfather. Therefore, it is a custom of Chassidim in general to mention a teaching from the Baal Shem Tov, or at least to mention him on Shavuos.
(According to most mesorahs, the Baal Shem Tov passed away on the first day of Shavuos; see Siddur Arizal of Rabbi Avraham Shimshon of Rashkov, p. 298; Rabbi Yitzchok Eizik Yehudah Yechiel Safrin of Komarno, Heikhal HaBerakhah, "Ki Seitzei," 129b; Sefer Baal Shem Tov, "Ki Savo," in Mekor Mayim Chaim, note 12; Rabbi Yosef Yitzchok of Lubavitch, Likutey Dibburim, Vol. III, p. 1054; Darkei Chaim vi-Shalom-Munkatch, Hil. Yom Tov, 527).
Likutey Moharan I, 56, sec. 7
This is a difficult excerpt from a complex lesson, but well worth studying, especially in preparation for the coming Yom Tov.
The holiday of Shavuos represents an extremely great and exalted level of consciousness, which is supernal loving-kindness and great compassion; for the extent of compassion depends upon the extent of divine perception (da'as). This is because at the Giving of the Torah, the Holy One, blessed be He, appeared as an Elder full of compassion" (Rashi on Exodus 20:2).[1]
"Elder" refers to one who possesses a composed mind (yishuv ha-da'as; see Kinim 3:6; Zohar III, 128b). This determines the extent of compassion, as we have stated. Thus, Shavuos [which commemorates the time when God was revealed as an "Elder full of compassion,"] is characterized by supernal loving-kindness and great compassion.
This is also the paradigm of the mikveh of Shavuos,[2] which is the aspect of the mikveh of the Fiftieth Gate—the highest gate of the Fifty Gates of Binah / Understanding,[3] the aspect of supernal loving-kindness and great compassion.
Therefore, the mikveh saves from all troubles, as it is written, "The Hope (Mikveh) of Israel, Who saves her in a time of trouble" (Jeremiah 14:8).[4] For it is supernal loving-kindness, which saves from all troubles. This is why the mikveh purifies from all impurities, as it is written, "And I will sprinkle upon you purifying water, and you will be purified" (Ezekiel 36:25).[5] For "there is no suffering without sin" (Shabbos 55a). Thus, the mikveh, which delivers from all trouble and all suffering, purifies from all forms of impurity and all sin.
This is the paradigm of MaN (Aramaic: manna),[6] which corresponds to the aspect of "exalted consciousness"; because the manna is the aspect of da'as.[7]
This corresponds to "an open statement (ma'amar pasu'ach), extended trustworthiness (ne'eman pashut)" (Shabbos 104a).[8] An "open statement" is the aspect of revealing da'as, for speech is the medium through which da'as is expressed; as it is written, "Da'as and understanding are from His mouth" (Proverbs 2:6).
In Egypt, da'as was in exile, as it is written, "However, I did not make Myself known to them by My Name YHVH (Exodus 6:3); thus, speech was also in exile. This is the aspect of [Moses's description of himself as] "difficult of speech and difficult of language" (ibid. 4:10).[9] However, when they left Egypt, when da'as went out of exile, speech came forth and "opened up." This is the meaning of an "open statement": speech opened up and revealed da'as.
Through the revelation of da'as, the perception of God's trustworthiness spreads forth and it becomes apparent that He is trustworthy—He promises and He acts. This is the aspect of "extended trustworthiness": His trustworthiness spreads forth. In Egypt, where da'as was in exile, His trustworthiness did not spread forth, and it was not apparent. Accordingly, Rashi explains the verse: " 'However, I did not make Myself known to them by My Name YHVH'—I was not known by My true quality." Since higher consciousness was not revealed in Egypt, His trustworthiness was not apparent; for loving-kindness depends upon da'as, as we have said.
This is the aspect of "ANOKHY" (Exodus 20:2),[10] the initial letters of which our Sages interpret to mean "Yehiva Kesiva Ne'emanim Amareha . . . My giving, My writing, Her statements are trustworthy" (Shabbat 105a).[11] [The initial letters of "ANOKHY" corresponds to this phrase.] Through the Giving of the Torah, the "statement" [i.e., holy speech] was opened and da'as was revealed, and through this, God's trustworthiness spread forth. This is the aspect of "ne'emanim amareha . . . her statements are trustworthy," corresponding to "extended trustworthiness (ne'eman pashut), an open statement (ma'amar pasu'ach)," discussed above.
This is also the aspect of MaN (manna), which is an acronym of "Ma'amar Ne'eman (a trusted statement)," corresponding to "an open statement (ma'amar pasu'ach), extended trustworthiness (ne'eman pashut)." For the manna embodies the paradigm of great da'as. Therefore, "the Children of Israel ate the manna for forty years" (Exodus 16:35)—because "at the age of forty, one gains understanding (binah, as in the Fifty Gates of Binah / Understanding)" (Avos 5:21).
1. In the Kabbalah, the term "elder (zaken)" is related to the sefirah of Keser, which transcends all harsh judgments and is the source of the Thirteen Divine Attributes of Mercy. These Thirteen Attributes are symbolized by the beard, which in Hebrew is "zakan." The word zakan is related to zaken, "elder."
2. A mikveh is a natural body of water or man-made pool that meets certain halakhic requirements, which enables a person or object to regain a state of ritual purity (taharah). This water is symbolically related to the "river that came forth from Eden," mentioned at the beginning of Genesis.
3. Our Sages state that the world was created through "Fifty Gates of Binah / Understanding," all but one of which were revealed to Moshe Rabbenu (Nedarim 38a). The Zohar and other kabbalistic works relate these Fifty Gates of Binah / Understanding to the fifty times that the Exodus is mentioned in the Torah (see Rabbi Moshe Cordovero, Shiur Komah, Hakdamah, Parshah 92). Thus, there is a deep connection between the revelation of the mysteries of creation and the Exodus, which culminated in the Giving of the Torah at Mount Sinai, when the entire nation attained prophecy. According to the Arizal (see Sha'ar ha-Kavannos, Shavuos, Drush 1), the mikveh into which it is customary to immerse on Shavuos morning is related to this awesome level of the Fiftieth Gate—which ultimately will be made available to all Israel with the proliferation of da'as in the Messianic Age.
4. The word mikveh also can mean "hope." Thus, the verse from Jeremiah, which refers to God as the "Hope of Israel," may be understood homiletically to allude to the mikveh in which one immerses to attain purity.
5. That is, just as God will purify all humanity through water in time to come, when divine knowledge will fill the world, so the mikveh purifies even today.
6. The word "MaN" is spelled "mem-nun." In context of this lesson, these letters are an acronym for "mikveh nun," the Mikveh of the Fiftieth Gate.
7. By eating the manna from heaven during their forty years in the desert, the Children of Israel attained higher levels of consciousness. The manna was the ideal food, possessing none of the spiritual or even physical problems associated with ordinary food.
8. The Gemara renders each letter of the Hebrew alphabet interpretively. This cryptic phrase is what it has to say about the letters mem and nun. The Rebbe goes on to elucidate this idea in keeping with his teaching about the exile and redemption of consciousness (da'as).
9. This refers to Moshe's speech impediment, which was only manifest during the period of Egyptian exile. After the Exodus, the Torah never again mentions this problem. This implies that Moshe stuttered because holy speech in a transpersonal sense was in exile in Egypt. With the Giving of the Torah at Mount Sinai, speech was rectified (Zohar II, 25b).
10. This is the first word of the Ten Commandments, which begin "ANOKHY / I am the Lord your God, Who brought you out of Egypt…" (ibid.).
11. The letters of the word "ANOKHY," when read backward, are an acronym of Yehiva Kesiva Ne'emanim Amareha . . . My giving, My writing, Her statements are trustworthy." This interpretation suggests that with the word "ANOKHY," God gave His approbation to the words that followed. The emphasis on the trustworthiness of God's word in this interpretation of the Talmudic Sages lends support to Rebbe Nachman's lesson.
Moshe Entered the Mist Likutey Moharan I, 115
Translated by Rabbi Moshe Mykoff
Annotated by Rabbi Chaim Kramer
© Breslov Research Institute
In this online version, we have presented the translation in bold and the commentary in non-bold typeface, except for headings.
"Vaya'amod Ha'am Meirachok (The people kept their distance) and Moshe entered the mist where God was." (Exodus 20-18)
The verse quoted from Exodus refers to the Revelation at Mount Sinai. The Israelites heeded God's command and kept their distance from the mountain while Moshe ascended and entered the mist to receive the Torah. This lesson speaks about ascending and entering into God's service, symbolized by receiving the Torah.
When a person who has spent all his days in materialism afterwards becomes inspired and wants go in the ways of God, the attribute of judgment then denounces him and prevents him from going in God's ways. It also arranges obstacles for him.
Attribute of judgement … obstacles: "Taste and see that God is good" (Psalms 34:9). That is, all that is good can be found wherever one finds God and comes close to Him. When a person has lived a materialistic life and then wishes to return to God, the attribute of judgment contests his benefiting from any good. "After all, he has not been good! Why should he be allowed to taste and enjoy anything good (God/spirituality)?" This is why even when people want to serve God, they encounter obstacles.
Yet, God "is one who desires kindness" (Micah 7:18), and He hides Himself, as it were, in this obstacle {see below}. Thus, someone who is wise will look at the obstacle and discover the Creator there. As we find in the Yerushalmi (Ta'anit 1:1): If anyone should ask you, "Where is your God?" answer him, "In the great city of Rome." As is said, "One calls to Me from Seir'' (Isaiah 21:11) . But someone who is not wise, when he sees the obstacle, he immediately retreats.'
"Seir" is the domain of Esav, under whose descendants, Edom/Rome, the Jewish people are exiled. God says that the prophet calls out to Him from the darkness of exile in Seir/Rome, asking when the Final Redemption is to begin. God's answer appears in the next verse (v. 12): The time is at hand, provided the people of Israel repent (see Rashi). The Talmud Yerushalmi (loc. cit.) learns from here that even in Rome—the darkest exile, in which it seems that holiness and spirituality can never be found—even there, God is present. When a person asks, "Where is God?" answer him, "He is right next to you. No matter how dark it is where you are, God is there, waiting for you to return to Him." This is the meaning of what Rebbe Nachman says, that because of His desire to do kindness, the Creator hides Himself in the very obstacles which He places before anyone seeking to come close to Him. All a person has to do is persevere and truly look for God in wherever he is at that moment!
Rebbe Nachman discusses this passage from Ta'anit in a number of lessons. See Likutey Moharan I, 33, and II, 12.
Now, an obstacle corresponds to cloud and mist. This is because a cloud and a mist are darkness, [and] ChoSheKh (darkness) connotes an obstacle. As is written (Genesis 22:16), "and you did not ChaSaKh (hold back)."
ChoSheKh ... ChaSaKh: God's angel called out to Avraham and praised him that he "did not chasakh (hold back)" Yitzchak from being sacrificed to God. The word chasakh connotes holding back, much as an obstacle holds a person back from serving God. Its root is the same as the word choshekh, the darkness or obstacles to vision created by clouds and mist. These are the dark and confusing moments of life, when a person feels that God is hidden from him.
Reb Noson explains often that, in reality, the main obstacles to spiritual development are obstacles of the mind, mental blocks. A person has awesome inner strength, he says, but his mind becomes "cloudy," confused and distraught because of his many problems. These obstacles of the mind are always the greatest opposition one finds to fulfilling his desire to serve God (Likutey Halakhot, Birkhat HaPeirot 4:4). Reb Noson writes that in his attempts to visit the Holy Land, he encountered awesome and numerous obstacles. Yet, the greatest of these obstacles were those of his own making—i.e., his own doubts and confusion (Yemey Moharnat II, 25).
This is the explanation of the verse:
The people kept their distance—For when they see the mist, the obstacle, they keep their distance.
This is because most people lack the da'at (holy knowledge) to realize that God is in the obstacle. Rather than seeing past the mist, they keep their distance.
and Moshe—He corresponds to the da'at (holy knowledge) of all Israel.
The Ari teaches that Moshe Rabeinu was the personification of da'at (Eytz Chaim 32:1). Because he possessed holy knowledge, he knew to continue searching for God despite the obstacles.
entered the mist where God was—In other words, into the obstacle, which is precisely where God is hidden.
Reb Noson appends the following:
We heard more on this from [Rebbe Nachman's] holy lips. He added an explanation of the earlier point, that God Himself hides Himself within the obstacle. He said:
God "loves justice" (Isaiah 61:8), and He also loves Israel. Yet, his love of Israel is greater than His love of justice (Zohar Ill, 99b).
The passage from the Zohar quoted in the text discusses Rosh Hashanah as a day of judgment. It teaches that even though justice demands a properly adjudicated judgment, and "God loves justice," nevertheless, God's love of Israel is greater than His love of justice. Therefore, He commanded the Jews to sound the shofar on Rosh Hashanah using a ram's horn. This recalls how Avraham, at God's bidding, selflessly offered Yitzchak on the altar, and then, again at God's bidding, replaced him with the ram that had become caught in the nearby thicket (Genesis 22). Sounding the shofar thus arouses God's mercy so that He overrides justice and invalidates the prosecutor's arguments.
We can see from this that when a person overcomes obstacles to his spiritual development, he draws mercy into the world. Thus, overcoming obstacles not only brings him knowledge and enables him to draw closer to God, but also mitigates decrees as a result of his good deeds (Rabbi Nachman of Tcherin, Tefilot v'Tachanunim I, 11).
Therefore, when the attribute of judgment denounces someone who is not worthy of drawing closer to God and prevents him from entering the path of life, so as to draw closer to the true tzaddik and the true path; and [what is more,] God Himself loves justice—when this occurs, God is obliged, as it were, to agree to arrange obstacles for him so as to keep him from the path of life. [These obstacles are] commensurate with what he deserves based on his evil deeds, in accordance with judgment and justice. For the Holy One cannot disregard the judgment, because God loves justice, as mentioned above.
However, since in truth God loves Israel, and that love for Israel is greater than the love for justice, what is the Holy One to do? For He is obliged, as it were, to agree to the obstacles which keep the person from the truth, because of the judgment and the justice that is upon him—for He loves justice. This notwithstanding, the ultimate truth is that God's will and desire is that this man nevertheless draw closer to Him. This is because, as mentioned, He loves Israel more than justice.
Therefore, God grants permission for obstacles to be arranged for him. But He Himself hides Himself, as it were, within the obstacles. And one who is wise will be able to find God within the obstacles themselves. For the truth is that there are no obstacles whatsoever in the world.
How can Rebbe Nachman say that there are no obstacles, when there is hardly a Jew alive incapable of personally attesting to their existence? The person who wants to purchase Tefillin but finds himself without money to do so, he knows about obstacles to spirituality. So does the person who works to comprehend some difficult Torah insight, but for whatever reason finds it beyond him. Or what about the obstacles to our spiritual development which we create for ourselves through laziness, anger, hard-heartedness and the like; not to mention those from parents, children, friends, etc., of which the Rebbe himself often spoke (see Likutey Moharan II, Foreword)? When Rebbe Nachman says that "there are no obstacles in the world," he means the following: Consider the purpose of these obstacles. Seemingly, they are intended to distance the person from God. But if God hides Himself in the obstacle, expecting the person to find Him there, they do not accomplish their purpose. Only a person who backs off when he encounters the obstacle will be defeated. The person who truly seeks will no doubt say to himself, "Can this be an obstacle to drawing close to God if God Himself is right next to me?" Therefore, in truth—for those seeking God—there are no such things as obstacles.
In the very force of the obstacles themselves, God is hidden. Thus, specifically through the obstacles themselves one is able to draw closer to the Holy One, for God is hidden there, as mentioned above.
Specifically through the obstacles themselves: Although it might seem so, this is not at all a superfluous comment. Previously, Rebbe Nachman explained that a person who is wise will find God in the obstacle. He will know that God is hidden there and will look for Him despite the "clouds" and "mist." What the Rebbe adds and emphasizes here is that precisely because God is hidden there, the obstacle itself becomes a vital key and vehicle for drawing closer to Him. This is similar to the relationship which man's soul has with his body. In order for the soul to develop and reunite with God on a spiritual level higher than the one it had at its origination, it must be challenged and tested. The stage for this testing is this world and the soul's entry into it via the physical body with all its accompanying needs, attachments and desires—all of which seem to present obstacles to spiritual development. "Using the body as a medium, the soul is able to form structures in the physical world that reveal Godliness concealed beneath the surface. These activities bring Godliness into the soul itself, benefiting it when it eventually leaves this world and returns to the higher spiritual realms" (Under the Table, Tsohar Publishing). The same came be said of all the obstacles in which God is hidden, waiting to be found.
"Specifically through the obstacles themselves" can also be understood in light of what Reb Noson writes about opposition to the tzaddik (see Lesson #114, note 10). He explains that this opposition conceals the tzaddik's great light, making it possible for the common person to draw close to the tzaddik without being overwhelmed by a light that is too great for him. As a result, anyone who so desires can benefit from the tzaddik by virtue of this concealment. In the same way, obstacles to spiritual development protect the person who seeks to come close to God, so that he is not suddenly overwhelmed by the great light of the Holy One. Rather, the "clouds" and "mist" help him create vessels with which to gradually absorb and benefit from that light.
Thus, this is the meaning of "and Moshe entered the mist"—the obstacle—"where God was."
"Even if the heavens were parchment,
All the trees were quills,
The seas and all waters were ink,
And all inhabitants of the earth were scribes and skilled writers,
His might eternal would remain beyond description.
Alone, the resplendent Master of heaven and earth
Founded the universe and garbed it in mystery…"
One of the highlights of Shavuos is the responsive chanting in the synagogue of Akdamus Milin, written by Rabbi Meir ben Yitzchak of Worms during the 11th century C.E. The hymn begins with these two Aramaic words, which mean "Before I speak…" (The author asks the Creator permission to utter His praise.) However, as a title, Akdamus Milin may be translated "Introduction to the Words," meaning the Divine Speech heard at Mount Sinai. Therefore it is usually read on Shavuos morning before the Torah reading, which describes the awesome experience of all Israel hearing the Ten Commandments at the foot of the desert mountain.
Rabbi Noson of Breslov (1780-1844) writes that Rabbi Nachman highly praised Akdamus.
"The Rebbe observed, 'Because the Jewish people are so immersed in and habituated to what is truly good, they don't fully appreciate the greatness of the sacred hymn of Akdamus, which we recite on Shavuos.'
"He went on to say, 'One who knows the loftiness of this poem of Akdamus, together with the melody to which it is commonly sung, realizes that this is something most wondrous and unique.'
"The Rebbe then chanted a few stanzas of Akdamus. He added, 'Akdamus is a song of cheshek – of love and desire for God.'
"The Rebbe said all of this on Shavuos, during the dairy meal [traditionally eaten after the morning service]. The second minyan was in the middle of their prayers in the synagogue, and the chazan was chanting Akdamus. That was when the Rebbe spoke with us about the loftiness of this hymn." (Sichot HaRan 256)
Rabbi Nachman clearly experienced Akdamus as an expression of the mutual love between the Jewish People and G-d. This love and desire is the pre-condition of prophecy, which is the essence of the Torah.
Continuing to expound upon this theme, Reb Noson also discusses the custom of reading Akdamus in his masterwork, Likkutei Halakhos:
"On Shavuos, we spiritually ascend to the supernal root of ratzon (will or desire). [An aspect of the sefirah of Keser (Crown), ratzon expresses the deepest will and desire of the soul for God, and God's corresponding will and desire, so to speak, for creation].
"Through this ascent, all profane wisdoms related to the natural order are transmuted to ratzon, due to the power of the revelation of ratzon that now becomes manifest. That is, we vividly perceive all existence and all that transpires as only a reflection of the Divine Will.
"Profane or 'natural wisdoms,' by contrast, are derived from the Aramaic tongue. [Aramaic is the language closest to leshon ha-kodesh, the 'holy tongue,' which is Hebrew. During the Talmudic period, Aramaic was used for everyday speech and writing.] On Shavuos, however, the aspect of ratzon is revealed to such an extent that even the Aramaic tongue, the source of 'natural wisdom,' becomes absorbed into the holy.
"This is why we recite Akdamus, which is an awesome expression of praise written specifically in Aramaic – for this transformation of the profane to the holy represents the fullest revelation of ratzon." (Likkutei Halakhos, Hilkhos Kaddish, 1)


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Desc: She's like a pillowy lewis black on helium.
"You know what I don't get? These liberals like gays AND Muslims! But Muslims KILL gays! What's with that?"
That made me laugh so hard. So, so hard.
She is genuinely baffled by the concept of respecting people and points of view that aren't the same as yours. And for good reason.
If you truly believe, then tolerating any people or ideas that contradict the Bible is basically evil. Given that the consequences are an eternity of unfathomable suffering, all rational true believers should be whatever it takes to impose their beliefs on others.
When she held up the bible, I did actually, literally laugh out loud. She brought a bible to an interview? Just to hold up once? Or do you think she had some passages marked for quotations.
She is Poe's law personified. I really cannot tell.
I can't tell either. I dated a girl that did this kind of thing for fun, but she was also all kinds of crazy (not always in a fun sence) in different ways.
"It doesn't matter what I think..."
If they had simply agreed and cut off the interview there I'd be applauding.
Then again, having a continuous loop of two boys kissing dominating the screen whenever she talks about overexposure of gays in media seems like they're deliberately taking the mickey.
Kicked in the head by a horse?
Heart attack but saved by a gay doctor.
Then she dies from another heart attack.
I just realized, milliseconds after posting, that we were not discussing how she should die.
Comeuppance, you made my night.
Someone shoved a buttered turkey into her head.
So she's not trolling I take it?
She made a career out of playing clueless airheads in comedy sketches. One possibility is she's turning her comedy into a lifestyle. Another possibility is it wasn't really an act in the first place.
The gay kiss loop is fantastic.
I know that I neglected pursuing the hathos implied by CNN's claim that this is breaking news but having only title, description and tags at my disposal I thought I'd go for the big fish.
Glad she received a dispensation for gluttony.
She stole that Bible from her hotel room.
If it were anyone else, I'd say they were abusing tranquilizers.
I love the "former SNL star" title. She will always be just that, because she will never do anything as culturally significant again.
Um, she was in a little movie called "UHF"? Don't hate.
I just want to know where her outrage was when the cheerleaders were kissing on that show- I'm fairly certain that behavior is just as gay. Also, how can anyone interact with that voice for any length of time without involving steak knives and lye?
Can't watch it. Please, someone tell me, at any point in the interview are the words "massive weight gain" uttered?
Or even "you hateful pig"?
She certainly knows a lot about the Good Book!
If I ever meet Norm she is all I want to talk about.
I'd wager there's a lot of things confusing her.


text:
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text:
BBC News Updated every minute of every day
Page last updated at 12:29 GMT, Monday, 16 March 2009
First North Korean pizzeria opens
It is unclear how many North Koreans will be able to try the pizzas
North Korea's first pizzeria has opened in the capital Pyongyang, according to a Japan-based newspaper.
Chefs were sent to Italy for training by leader Kim Jong-il, who said North Koreans should be able to try the world's best foods, said Choson Sinbo.
Many people in the secretive communist state live in poverty and rely on food aid, but a wealthy elite can afford a more luxurious lifestyle.
An estimated two million North Koreans have died in famines since the 1990s.
Mr Kim's expensive tastes in food have often been commented on by those who have met him. He is believed to have a fondness for caviar, French wines, shark fin soup and cognac.
But the new restaurant's manager, Kim Sang-soon, said Mr Kim believed all North Koreans should "also be allowed access to the world's famous dishes".
I knew well from television and publications that pizza and spaghetti are world famous food, but it is the first time that I've tasted it
Jong Un-suk, customer
Making pizza for Kim Jong-il
"He then called for the establishment of a restaurant specialising in Italian food," Kim Sang-soon told the Choson Sinbo.
The pro-North Korean newspaper said the restaurant, which imports its flour, butter and cheese from Italy, had been busy since opening in December.
Many customers were trying Italian food for the first time.
"I knew well from television and publications that pizza and spaghetti are world famous food, but it is the first time that I've tasted it," said one diner, Jong Un-suk.
Pyongyang already has a successful fried chicken outlet, opened in 2007 and, its owners say, taking £1,000 a day.
Last year, chefs were flown to Naples and Rome to learn how to create authentic pizzas and pasta dishes, returning to North Korea to perfect them through "trial and error", said Kim Sang-soon.
FROM THE BBC WORLD SERVICE
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More from BBC World Service
But it is possible the new restaurant has been at least a decade in the planning.
Italian chef Ermanno Furlanis was flown to North Korea in 1997 along with special pizza ovens.
In 2004, he described to the BBC how he had given lessons to three army officers who took copious notes and asked detailed questions such as how far apart olives should be placed on each pizza.
Mr Furlanis said Kim Jong-il may even have visited one of the training sessions, being held on a ship anchored offshore.
"I am not in the position to say whether it really was him, but our chef, who had no reason to fib, was, for the space of several minutes, utterly speechless," Mr Furlanis said.
"He said he felt as if he had seen God, and I still envy him this experience."
It is, however, unlikely that many ordinary people will be able to eat in the new restaurant.
North Korea is among the world's poorest countries, relying on international food aid to feed its people.
According to the World Food Programme, up to nine million North Koreans were facing urgent food shortages this winter.
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Posted in New York Theater, Theater Online, Theater Reviews
What If If Only. Caryl Churchill's ghostly new play, via NAATCO
Author: New York Theater Published Date: June 8, 2021 Leave a Comment on What If If Only. Caryl Churchill's ghostly new play, via NAATCO
What I can say about "What If If Only?" In short:
It's a new play by Caryl Churchill, 82, who some consider the world's greatest living playwright, and among the most elusive, whose work over the last half century is consistently inventive (as New York theatergoers have been able to sample first-hand in productions over the past few years of "Cloud Nine" and "Love and Information" — both of which I found delightful — as well as "Light Shining on Buckinghamshire" — which I didn't.)
"What If If Only" is a production of the National Asian American Theatre Company, which is live-streaming it every evening through Saturday, June 12. It is "realized" by the team of director Les Waters (known most recently for his otherwordly work with Lucas Hnath on "The Thin Place" and "Dana H.") and multimedia theater artist Jared Mezzocchi (increasingly acclaimed for his work on such pandemic-era digital theater as "Russian Troll Farm.")
The first of the play's five cast members to speak is Mia Katigbak, who portrays a character identified in the program as S. "I was reading about this man who spent 10 years trying to paint an apple so it looked just like an apple," she begins. "Then he spent seven years trying to paint an apple so it looked nothing like an apple. Then he died." She wonders what kind of apple, and if he had lived would he have started in on an orange, and then asks how hard could it be to paint something that looks nothing like an apple.
These are funny thoughts. but she is apparently saying them to a character who is himself dead, identified in the program as F (portrayed by Bernard White), but who identifies himself to S by saying: "I'm the ghost of a future that never happened." This is cryptic, yes, but poignant.
And that's what I can say about the rest of "What If If Only," which seems a contemplation of grief and loss and loneliness, but not necessarily the death of specific, human loved ones but the loss of possibilities, of civilization, of Nature. It's less a story with characters, than a feeling; in the world of "What If If Only," everything feels short-lived.
That includes the play itself. "What If If Only" is 14 minutes long. Tickets are $15.
← 4 new Broadway openings: Lehman Trilogy, Skeleton Crew, Paradise Square, How I Learned to Drive. #OffBroadway is open NOW. #Stageworthy News
"Broadway you're finally coming back": Watch Lin-Manuel Miranda lead quick-hit homage →


text:
\section{Introduction}
Recently, various four-dimensional models embedded in higher dimensional spacetime have been greatly investigated \cite{ExDim}. Their spectra generally include Kaluza--Klein (KK) states, which carry nonzero momentum in extra-dimensions. As an example, let us consider a circle compactification of five-dimensional gauge theory with a massless matter field. The effective four-dimensional theory has a tower of KK modes of the gauge field, say $A_\mu^{(n)}$, and that of the matter field, say $\psi^{(n)}$, where $n$ runs over the integers and $\mu$ runs over $0,1,2,3$. The states $A_\mu^{(n)}$ and $\psi^{(n)}$ carry fifth dimensional momentum, $n/R$, where $R$ is the compactification radius. Then $A_\mu^{(n)}$ and $\psi^{(n)}$ with nonzero $n$ are KK states. In this paper, we investigate the stability of KK states.

A state $A$ is kinematically unstable and decays into states $B$ and $C$ when the charges are conserved in the process and their masses satisfy the inequality $M(A)\geq M(B)+M(C)$. In the case of the five-dimensional model above, masses of $A_{\mu}^{(n)}$ and $\psi^{(n)}$ are classically $\abs{n}/R$. Thus for $n\!\!>\!\!1$, $A_{\mu}^{(n)}$ can decay to $A_{\mu}^{(n-1)}$ and $A_{\mu}^{(1)}$ and $\psi^{(n)}$ can decay to $A_{\mu}^{(n-1)}$ and $\psi^{(1)}$. Similar decay processes occur for $n\!\!<\!\!1$. From these, we see that the stable KK states are $A_{\mu}^{(\pm 1)}$ and $\psi^{(\pm 1)}$. This result is supported by perturbative analysis in \cite{ST}, where the inequality of masses in various models are evaluated under the one-loop correction. On the other hand, nonperturbative behavior of the KK spectrum was found in the strong coupling limit of a supersymmetric extension of the model \cite{Ohtake3}. In \cite{Ohtake3}, the KK spectrum of a circle compactification of the five-dimensional $\mathcal{N}\!=\!2$ supersymmetric model with gauge group $SU(2)$ and $N_f\!=\!5,6,7$ massless fundamental matter fields was studied in the strong coupling limit. The four-dimensional effective theory possesses $\mathcal{N}\!=\!2$ supersymmetry, so that the exact mass formula is derived by using Seiberg--Witten theory \cite{SW}. In addition, the theory has the D3-brane probe realization \cite{BDS}, where the inequality is diagammatically evaluated by using string junctions \cite{BF1}. By using these techniques, it was shown that $A_{\mu}^{(n)}$ can decay to $A_{\mu}^{(n-1)}$ and $A_{\mu}^{(1)}$ similar to the perturbative result, while $\psi^{(n-1)}$ decays easier than $\psi^{(n)}$ in a certain region of vacuum moduli space.

Now we know that the perturbative KK spectrum is different from the spectrum in the strong coupling limit. How does the spectrum change as the five-dimensional coupling constant $g_5$ varies from 0 to $\infty$? To answer the question, we shall generalize the analysis in \cite{Ohtake3} to the case with finite $g_5$. In section 2,  we derive the exact mass formula for finite $g_5$, using Seiberg--Witten theory. From the mass formula and the D3-brane probe realization, we determine the stability of KK modes in section 3. As a result, we show that the nonperturbative behavior also appears in the case of the finite coupling constant. As we decrease $g_5$, the region where the nonperturbative behavior appears becomes small. As we take the limit $g_5\to 0$, the region disappears and the perturbative spectrum is reproduced.

\section{Seiberg--Witten solution}
\subsection{Seiberg--Witten curve}
Five-dimensional $\mathcal{N}\!=\!1$ supersymmetric gauge theory compactified on a circle is effectively described by four-dimensional $\mathcal{N}\!=\!2$ supersymmetric gauge theory. It includes an adjoint complex Higgs scalar field $\phi$ as a superpartner of the gauge field, and has a vacuum moduli space parametrized by the vacuum expectation value of $\phi$. The low energy effective Lagrangian and the mass formula are derived from a Seiberg--Witten curve \cite{SW}.

For the theory with gauge group $SU(2)$ and $N_f$ matter fields in the fundamental representation, which we refer to as quarks, the Seiberg--Witten curve is written as \cite{MNW}
\begin{equation}
y^2 = x^3+f(u)x+g(u), \label{eqn:SW0}
\end{equation}
\begin{align}
f(u) &= \sum_{i=0}^4 a_i u^i,&
g(u) &=\sum_{i=0}^6 b_i u^i,
\end{align}
where $u \!=\!\expect{\Tr\phi^2}$, a gauge invariant moduli parameter, which takes a value on $CP^1$. Constants $a_i$ and $b_i$ depend on the parameters of the theory such as the five-dimensional coupling constant $g_5$, the compactification radius $R$, and masses of the matter fields $m_i$ ($i\!=\!1,\ldots, N_f$). In this subsection, we shall determine these constants. For simplicity, let us assume $N_f\!=\!4$ and $m_i\!=\!0$ for all $i$.

The zero points of the discriminant of \eqref{eqn:SW0},
\begin{equation}
\Delta(u) = 4f(u)^3+27g(u)^2,
\end{equation}
are determined from global symmetry \cite{HO}. The correspondence between global symmetry and zeros of $\Delta(u)$ is listed in \cite{Kodaira} and \cite{dWHIZ}. Since our model has the flavor symmetry $SO(8)$, we obtain that $a_0$ and $b_0$ are to be vanished and $\Delta(u)$ is proportional to $u^6$ \cite{Kodaira}. In addition, the symmetry is extended to broken affine $SO(8)$ \cite{YY}. This is because the states carry not only $SO(8)$ charges but also the KK charge $n$. In other words, an $SO(8)$ multiplet has copies labeled by an integer $n$. This is just the structure of affine $SO(8)$ multiplets. The affine symmetry is broken at the scale $1/R$ because the copies have different masses. The broken affine symmetry requires two additional zero points \cite{dWHIZ}. From these restrictions, we conclude that the curve of our model is
\begin{equation}
\begin{split}
y^2
&= x^3+\left\{a_2+u\left(a_3-\frac{3u}{L^4}\right)\right\}u^2x \\
&\quad +\frac{L^6}{216}\left(a_3-\frac{6u}{L^4}\right)\left\{a_3^2+\frac{24a_3u}{L^4}+\frac{36}{L^4}\left(a_2-\frac{2u^2}{L^4}\right)\right\}u^3.
\label{eqn:SW1}
\end{split}
\end{equation}
To simplify the curve, we scale and shift the variables as
\begin{align}
y &\to \frac{1}{24\sqrt{3}}y,&
x &\to \frac{1}{12}\left\{x-\frac{L^2}{3}\left(a_3-\frac{u}{L^4}\right)u\right\},&
u &\to \frac{1}{6}u,
\end{align}
and set $a_3=b/L^2$ and $a_2=(3c^2-b^2)/12$. Then we obtain a simple form,
\begin{equation}
y^2 = x^3+\left(\frac{u}{L^2}-b\right)ux^2+c^2u^2x. \label{eqn:SW2}
\end{equation}
Then the discriminant is given by
\begin{equation}
\Delta(u) = c^4u^6\left\{u-(b+2c)L^2\right\}\left\{u-(b-2c)L^2\right\}.\label{eqn:disc}
\end{equation}

Next we consider the constants $b$, $c$ and $L$. They are functions of $g_5$ and $R$. In the following, we derive explicit forms of the functions by matching the curve \eqref{eqn:SW2} with that of two limits. We choose $R/g_5^2$ and $R$ as a set of independent variables, and complexify $R/g_5^2$ to $\tau=4\pi iR/g_5^2+\theta/2\pi$, the bare coupling constant of four-dimensional effective theory.

Firstly, we consider a limit $R\to 0$ with fixed $\tau$. In this limit,
the theory is reduced to four-dimensional $\mathcal{N}\!=\!2$ $SU(2)$
gauge theory with $N_f\!=\!4$ massless quarks, and the coupling constant
$\tau$. Its Seiberg--Witten curve is known as \cite{SW}
\begin{equation}
y^2 = x^3-\frac{1}{4}g_2(\tau)u^2x-\frac{1}{4}g_3(\tau)u^3, \label{eqn:SWref}
\end{equation}
where $g_2(\tau)$ and $g_4(\tau)$ are the Eisenstein series:
\begin{align}
g_2(\tau) &= \frac{60}{\pi^4}\sum_{(m,n)\in Z^2_{\neq 0}}\frac{1}{(m+n\tau)^4},&
g_4(\tau) &= \frac{140}{\pi^6}\sum_{(m,n)\in Z^2_{\neq 0}}\frac{1}{(m+n\tau)^6}.
\end{align}
The mass dimensions of $y$, $x$ and $u$ in \eqref{eqn:SWref} are 3, 2 and 2, respectively. Setting the same in \eqref{eqn:SW2}, we find that the mass dimensions of $b$ and $c$ are 0 and that of $L$ is 1. Hence $b$ and $c$ depend only on $\tau$ and then $L$ is written as $1/R$ times a function of $\tau$, say $f(\tau)$. The function $f(\tau)$ is removed from the curve by scaling parameters as $u\to f(\tau)u$, $b\to b/f(\tau)$ and $c\to c/f(\tau)$. Altogether rearranging the curve \eqref{eqn:SW2} yields the following equation:
\begin{equation}
y^2 = x^3+\left(R^2u-b\right)ux^2+c^2u^2x \label{eqn:SW3}.
\end{equation}
Now we take the limit $R\to 0$ in \eqref{eqn:SW3} and compare with \eqref{eqn:SWref}. As we shift $x$ as $x\to x-bu/3$ in \eqref{eqn:SWref}, we see that
\begin{align}
b &= -3e_i(\tau) \label{eqn:b}\\
c^2 &= 3e_i^2(\tau)+e_1(\tau)e_2(\tau)+e_2(\tau)e_3(\tau)+e_3(\tau)e_1(\tau).
\label{eqn:c}
\end{align}
Here $e_i(\tau)$ ($i\!=\!1,2,3$) are the solutions of the equation $x^3-g_2(\tau)x/4-g_3(\tau)/4=0$. They are written as
\begin{equation}
\begin{aligned}
e_1(\tau) &= \frac{1}{3}(-\theta_1^4(\tau)+2\theta_3^4(\tau)),\\
e_2(\tau) &= \frac{1}{3}(-\theta_1^4(\tau)-\theta_3^4(\tau)),\\
e_3(\tau) &= \frac{1}{3}(2\theta_1^4(\tau)-\theta_3^4(\tau)), \label{eqn:es}
\end{aligned}
\end{equation}

where $\theta_1$ and $\theta_3$ are
\begin{align}
\theta_1(\tau) &= \sum_{n\in Z}e^{i\pi\tau (n+1/2)^2},&
\theta_3(\tau) &= \sum_{n\in Z}e^{i\pi\tau n^2}. \label{eqn:theta}
\end{align}

Secondly, we consider the limit $g_5\to\infty$ with zero $\theta$-angle and fixed $R$. In this limit, flavor symmetry $SO(8)$ is enhanced to $E_5$ \cite{Seiberg} and the curve should be \cite{MNW,YY}
\begin{equation}
y^2 = x^3+(R^2u-4)ux^2+4u^2x. \label{eqn:SWref2}
\end{equation}
Now we take the limit in the curve \eqref{eqn:SW3}. From \eqref{eqn:es}, \eqref{eqn:theta}, and the relations $e_1(\tau)=e_2(-1/\tau)/\tau^2$, $e_2(\tau)=e_1(-1/\tau)/\tau^2$ and $e_3(\tau)=e_3(-1/\tau)/\tau^2$, we see that $e_1(\tau)\sim -1/3\tau^2$, $e_2(\tau)\sim 2/3\tau^2$ and $e_3(\tau)\sim -1/3\tau^2$ in the limit. Thus $b\sim 1/\tau^2$ and $c^2\sim 0$ when $i$ in \eqref{eqn:b} and \eqref{eqn:c} is $1$ or $3$, while $b\sim 2/\tau^2$ and $c^2\sim 1/\tau^4$ for $i\!=\!2$. In the former case, we cannot make \eqref{eqn:SW3} coincide with \eqref{eqn:SWref2}. In the latter case, we make it by scaling parameters as $x\to x/4\tau^4$, $y\to y/8\tau^6$ and $u\to u/2\tau^2$. Then we choose $i\!=\!2$ in \eqref{eqn:b} and \eqref{eqn:c}. Thus we have
\begin{align}
b &= \theta_1^4(\tau) +\theta_3^4(\tau), \label{eqn:bf}\\
c &= \theta_1^2(\tau)\theta_3^2(\tau). \label{eqn:cf}
\end{align}

In summary, the Seiberg--Witten curve of our model is \eqref{eqn:SW3}, where $b$ and $c$ are given by \eqref{eqn:bf} and \eqref{eqn:cf}. Its discriminant is \eqref{eqn:disc} with $L\!=\!1/R$. The zero points of $\Delta (u)$ are located at $u\!=\!0$ and $(b\pm 2c)/R^2$. It is known that extra massless states appear at each zero point \cite{SW}. For simplicity, we set $R\!=\!1$ in the following.

\subsection{Mass formula}
From the Seiberg--Witten curve \eqref{eqn:SW3}, we shall derive the mass formula of stable states called BPS states. For this purpose, we derive the periods of the curve,
\begin{equation}
\Pi(u)=
\begin{pmatrix}
\omega_D(u) \\
\omega(u)
\end{pmatrix}
=
\begin{pmatrix}
\oint_\beta\frac{dx}{y} \\
\oint_\alpha\frac{dx}{y}
\end{pmatrix}, \label{eqn:pi}
\end{equation}
where $\alpha$ and $\beta$ are the homology cycles on the torus given by \eqref{eqn:SW3} with a fixed $u$.

The periods $\Pi(u)$ are determined from the Picard--Fuchs equation,
\begin{equation}
\left\{\frac{d^2}{du^2}
+\frac{3u^2-4bu+b^2-4c^2}{u(u-b-2c)(u-b+2c)}\frac{d}{du}
+\frac{4u^2-2bu-b^2+4c^2}{4u^2(u-b-2c)(u-b+2c)}\right\}\Pi(u)=0.\label{eqn:period0}
\end{equation}
As we set $\Pi(u)=u^{-1/2}k(w)$ with $w=-\left\{u-(b+2c)\right\}/4c$, the equation becomes
\begin{equation}
\frac{d^2 k}{dw^2}
+\frac{1-2w}{w(1-w)}\frac{dk}{dw}
-\frac{1/4}{w(1-w)}k
=0.
\end{equation}
This is the standard hypergeometric equation of $\alpha\!\!=\!\!\beta\!\!=\!\!1/2$ and $\gamma\!=\!1$. It has two independent solutions,
\begin{align}
K(w) &= \int_{-i\infty}^{i\infty}\frac{ds}{2\pi i}
\left\{\Gamma(-s)\Gamma(\frac{1}{2}+s)\right\}^2(1-w)^s, \label{eqn:K}\\
K'(w) &= \int_{-i\infty}^{i\infty}\frac{ds}{2\pi i}
\left\{\Gamma(-s)\Gamma(\frac{1}{2}+s)\right\}^2w^s. \label{eqn:Kd}
\end{align}
Series expansions of $K(w)$ and $K'(w)$ for $\abs{w}<1$, $\abs{1-w}<1$ and $\abs{1/w}<1$ are easily derived. For instance, the expansions for $\abs{w}\!<\!1$ are
\begin{align}
K(w) &= \pi\sum_{n=0}^{\infty}
\left\{\frac{\Gamma(\frac{1}{2}+n)}{n!}\right\}^2w^n, \label{eqn:EK}\\
K'(w) &= -\sum_{n=0}^{\infty}\left\{\frac{\Gamma(\frac{1}{2}+n)}{n!}\right\}^2w^n
\left\{\log w+4\sum_{r=0}^{n-1}\left(\frac{1}{2r+1}-\frac{1}{2r+2}\right)-2\log 4\right\}.\label{eqn:EKd}
\end{align}
The periods are given by linear combinations of the functions,
\begin{equation}
\Pi(u) = u^{-\frac{1}{2}}
\begin{pmatrix}
c_1 & c_2 \\
c_3 & c_4
\end{pmatrix}
\begin{pmatrix}
K(w) \\
K'(w)
\end{pmatrix}.
\end{equation}
Coefficients $c_1, \ldots, c_4$ are determined by direct calculation of elliptic integrals \eqref{eqn:pi} for $\abs{w}\!<\!1$ and comparing the result with the expansions \eqref{eqn:EK} and \eqref{eqn:EKd}. Indeed we have
\begin{equation}
\begin{pmatrix}
c_1 & c_2 \\
c_3 & c_4
\end{pmatrix}
=\frac{1}{\sqrt{c}\,\pi^2}
\begin{pmatrix}
2\pi & \phantom{m} & 0 \\
-\pi-2i\log 4 & \phantom{m} & -i\pi
\end{pmatrix}.
\end{equation}

The periods undergo monodromy around zeros of $\Delta(u)$. The monodromy matrices acting on $\Pi(u)$ around $u\!=\!0$, $b-2c$ and $b+2c$ are
\begin{align}
M_0 &= \begin{pmatrix}-1&0\\0&-1\end{pmatrix}, &
M_{-}& = \begin{pmatrix}3&4\\-1&-1\end{pmatrix}, &
M_{+}& = \begin{pmatrix}1&0\\-1&1\end{pmatrix},
\end{align}
respectively. From these matrices, we can determine what kind of states becomes massless at the zeros; when the monodromy matrix around a first order zero is
\begin{equation}
M_{(p,q)} =
\begin{pmatrix}
1-pq & \phantom{m} & p^2 \\
-q^2 & \phantom{m} & 1+pq
\end{pmatrix},
\end{equation}
a state $(p,q)$, whose electric and magnetic charges of unbroken $U(1)$ gauge symmetry are $p$ and $q$ respectively, becomes massless. Thus we see that $(2,-1)$ becomes massless at $u\!=\!b-2c$ and $(0,1)$ at $u\!=\!b+2c$. Moreover, six states become massless simultaneously at $u\!=\!0$, the sixth order zero. Since $M_0$ is expressed as $M_{(1,0)}^4M_{(2,-1)}M_{(0,1)}$, the massless states are $(2,-1)$, $(0,1)$ and four $(1,0)$.

Now we can write down the mass formula. It is described by the integration of the periods by $u$ \cite{SW}. Each bound of the integrals is decided in order to reproduce the extra massless states at the zero points correctly. Then the mass formula of a state with the electric and magnetic charges $(p,q)$ and the charges of broken affine symmetry related to the singularities at $u\!=\!b\pm2c$, say $n_1$ and $n_2$, is given by
\begin{align}
M_{(p,q,n_1,n_2)}(u) &= \abs{Z_{(p,q,n_1,n_2)}(u)}, \label{eqn:mass}\\
Z_{(p,q,n_1,n_2)}(u) &= pa(u)-qa_D(u)+n_1s_1+n_2s_2, \label{eqn:central}
\end{align}
where
\begin{align}
a_D(u) &= \int_0^{u}\!\!\omega_D(u')du',\\
a(u) &= \int_0^{u}\!\!\omega(u')du',\\
s_1 &= \int_0^{b+2c}\!\!\omega_D(u)du=8\pi\arcsin\sqrt{\frac{b+2c}{4c}},\\
s_2 &= -\int_0^{b-2c}\!\!\left\{2\omega(u)+\omega_D(u)\right\}du
   =8\pi\arcsin\sqrt{\frac{b-2c}{4c}}.
\end{align}
\piccaptionoutside
\piccaption{\footnotesize Three brunch cuts.\label{setup}}
\parpic[r]{\includegraphics[bb=50 50 220 201,width=200pt,clip]{setup.eps}}\picskip{14}
In the following,  we evaluate the values of $a$ and $a_D$ by means of the numerical integration on {\it Mathmatica}. For simplicity, we assume that the $\theta$-angle is zero. Then $b$ and $c$ are real, $c\!>\!0$ and $b\!\!>\!\!2c$. Hence the zeros of $\Delta(u)$, $u\!=\!0$, $b-2c$ and $b+2c$, are aligned from the left on the real axis of the $u$-plane. We set the branch cuts of $a_D$ and $a$ from these zeros to $\infty$ along the real axis as depicted in Fig.\ref{setup}. When we cross each cut from the lower half $u$-plane, \\$^t\!(a_D(u),a(u),s_1,s_2)$ is changed by the matrices
\begin{align}\hspace{-1em}
\widetilde{M}_0 &= \left(\begin{smallmatrix}-1&0&\phantom{0}0\phantom{0}&\phantom{0}0\phantom{0}\\0&-1&0&0\\0&0&1&0\\0&0&0&1\end{smallmatrix}\right), &
\widetilde{M}_{-} &= \left(\begin{smallmatrix}-1&-4&-2&\phantom{0}0\phantom{0}\\1&3&1&0\\0&0&1&0\\0&0&0&1\end{smallmatrix}\right), &
\widetilde{M}_{+} &= \left(\begin{smallmatrix}\phantom{0}1\phantom{0}&\phantom{0}0\phantom{0}&\phantom{0}0\phantom{0}&0\\1&1&0&-1\\0&0&1&0\\0&0&0&1\end{smallmatrix}\right)
\end{align}
for the cut from $u\!=\!0$, $b-2c$ and $b+2c$, respectively. To conserve \eqref{eqn:central}, we should change the charges $^t\!(p,q,n_1,n_2)$ simultaneously. The matrices acting on $^t\!(p,q,n_1,n_2)$ are given by
\begin{align}\hspace{-1em}
{K}_0 &= \left(\begin{smallmatrix}-1&0&\phantom{0}0\phantom{0}&\phantom{0}0\phantom{0}\\0&-1&0&0\\0&0&1&0\\0&0&0&1\end{smallmatrix}\right),&
{K}_{-} &= \left(\begin{smallmatrix}-1&-4&\phantom{0}0\phantom{0}&\phantom{0}0\phantom{0}\\1&3&0&0\\-1&-2&1&0\\0&0&0&1\end{smallmatrix}\right),&
{K}_{+} &= \left(\begin{smallmatrix}1&\phantom{0}0\phantom{0}&\phantom{0}0\phantom{0}&\phantom{0}0\phantom{0}\\1&1&0&0\\0&0&1&0\\-1&0&0&1\end{smallmatrix}\right).
\label{eqn:mono}
\end{align}

\section{Stability of KK modes}
Four-dimensional theory described by a Seiberg--Witten curve \eqref{eqn:SW0} appears in type IIB string theory as the world volume theory of a D3-brane probe in a 7-brane background \cite{BDS}. For our model, we employ the background constructed from six 7-branes $[1,0]^4[2,-1][1,0]$ at $z\!=\!0$, a 7-brane $[2,-1]$ at $z\!=\!b-2c$, and a 7-brane $[0,1]$ at $z\!=\!b+2c$. Here $z$ is a complex coordinate of the space transverse to the 7-branes, $[1,0]$ denotes a D7-brane, and $[p,q]$ denotes an $SL(2,Z)$-dual 7-brane \cite{Schwarz}. The metric on the $z$-plane is given by \cite{cosmic}
\begin{equation}
ds^2 = \Image\widetilde{\tau}(z)\abs{\frac{da(z)}{dz}dz}^2,
\end{equation}
where $\widetilde{\tau}(z)\!=\!da_D(z)/da(z)$. In this background, the world volume theory of a D3-brane probe located at $z=u$ is our model with the moduli parameter $u$. States of the model correspond to strings ending on the D3-brane. Therefore, the spectrum of states corresponds to the spectrum of strings which can end on the D3-brane probe. Then to find the spectrum of KK modes, we study the spectrum of corresponding strings.

In IIB string theory, there appear a fundamental string, $(1,0)$, and its $SL(2,Z)$-dual strings, $(p,q)$. A string $(p,q)$ has its ends on a D3-brane or a 7-brane with the same charges, $[p,q]$. In addition, strings can merge each other and make a string junction \cite{Schwarz}. Thus there are three kinds of strings ending on the D3-brane probe: a string connecting a 7-brane and the D3-brane, a string with the both ends on the D3-brane, and a string emanating from a string junction and ending on the D3-brane. Some strings are related to string junctions transitionally, due to the string creation at 7-branes \cite{transit}. In any case, a string $(p,q)$ ending on the D3-brane is detected as a state with the electric charge $p$ and the magnetic charge $q$. Especially, a string $(1,0)$ connecting $[1,0]$ at $z=0$ and the D3-brane corresponds to a quark, and a string $(1,0)$ with the both ends on the D3-brane corresponds to a gauge field. The winding number of a string around the 7-branes is equivalent to the KK charge $n$ \cite{MOY}.

To be stable, a string stretches along a geodesic that minimizes the string mass. The mass of a string $(p,q)$ along a curve $C$ is given by
\begin{equation}
\int_CT_{(p,q)}ds = \int\abs{dZ_{(p,q,0,0)}},
\end{equation}
where $T_{(p,q)}=\abs{p-q\widetilde{\tau}}/\sqrt{\Image\widetilde{\tau}}$, the tension of $(p,q)$ \cite{Schwarz}. In order to minimize this, points on a geodesic emanating from $z\!=\!z_0$ satisfy the equation
\begin{equation}
\Arg\left\{Z_{(p,q,0,0)}(z)-Z_{(p,q,0,0)}(z_0)\right\} = \phi. \label{eqn:geodesic}
\end{equation}
Here $\phi$ is a constant between $0$ and $2\pi$. It takes the same value for geodesics of the strings in a stable junction \cite{BF1}. Then, the mass of a string junction constructed from $n_1(2,-1)$ from $z\!=\!b-2c$, $n_2(0,1)$ from $z\!=\!b+2c$, $(p-2n_1,q+n_1-n_2)$ from $z\!=\!0$ and an outgoing string $(p,q)$ coincides with \eqref{eqn:mass} when the outgoing string ends on the D3-brane at $z\!=\!u$. Thus the junction corresponds to a state with the charges $(p,q,n_1,n_2)$. Note that the geodesic equation of the outgoing string $(p,q)$ is rewritten as
\begin{equation}
\Arg\{Z_{(p,q,n_1,n_2)}(z))\} = \phi. \label{eqn:geod}
\end{equation}
Hereinafter, we refer to the string obeying \eqref{eqn:geod} as $(p,q,n_1,n_2)$. When a string $(p,q,n_1,n_2)$ crosses branch cuts, it undergoes monodromy described by the matrices \eqref{eqn:mono}.

Let us notice that $\phi$ parameterizes the direction of geodesics. As
$\phi$ varies, the geodesic \eqref{eqn:geodesic} moves around the point
$z\!=\!z_0$ and sweeps some region in the $z$-plane. When the region
includes a point $z\!=\!u$, the string can end on the D3-brane probe at
$z\!=\!u$ and is detected as a stable state. Therefore, the region in
the $z$-plane through which the geodesic of a string passes corresponds
to the region in the moduli $u$-plane where the corresponding state is
stable \cite{BF1}. Then in the following, we seek the regions of KK modes of quarks $\psi^{(n)}$, unbroken $U(1)$ gauge fields $A_\mu^{(n)}$ and $W$-bosons $W_\mu^{(n)}$ by evaluating \eqref{eqn:geodesic} and \eqref{eqn:geod} for corresponding strings. In the following, we assume $b-2c\!=\!4$ and $b+2c\!=\!6$ unless we explicitly state otherwise.

\begin{figure}[t]
\begin{center}
\includegraphics[bb=50 50 274 258,width=360pt,clip]{GroundStates.eps}
\end{center}
\caption{\footnotesize The string which corresponds to a quark KK zero mode $\psi^{(0)}$ sweeps out whole of the $z$-plane. This result means that $\psi^{(0)}$ exists stably for any value of the moduli parameter $u$.}
\label{GroundStates}
\end{figure}%
\paragraph*{Quarks}
We now consider the cases of quarks. First of all we consider $\psi^{(0)}$. It corresponds to a string $(1,0)$ emanating from $z\!=\!0$, that is, $(1,0,0,0)$. The geodesics for various $\phi$ are evaluated as depicted in Fig.\ref{GroundStates}. From the figure, we see that the string sweeps all the $z$-plane. Thus we can conclude that $\psi^{(0)}$ is stable for all the moduli $u$-plane.

\begin{figure}[t]
\begin{center}
\begin{tabular}{ccc}
{\scriptsize A}\hspace{-1em}\includegraphics[bb=50 50 220 210,width=140pt,clip]{FirstPlot1.eps}&\hspace{-1.5em}
{\scriptsize B}\hspace{-1em}\includegraphics[bb=50 50 220 210,width=140pt,clip]{FirstPlot2.eps}&\hspace{-1.5em}
{\scriptsize C}\hspace{-1em}\includegraphics[bb=50 50 220 210,width=140pt,clip]{FirstPlot3.eps}\\
{\scriptsize D}\hspace{-1em}\includegraphics[bb=50 50 220 210,width=140pt,clip]{FirstPlot4.eps}&\hspace{-1.5em}
{\scriptsize E}\hspace{-1em}\includegraphics[bb=50 50 220 210,width=140pt,clip]{FirstPlot5.eps}&\hspace{-1.5em}
{\scriptsize F}\hspace{-1em}\includegraphics[bb=50 50 220 210,width=140pt,clip]{FirstPlot6.eps}\\
\end{tabular}
\end{center}
\caption{\footnotesize The string geodesics corresponding to $\psi^{(n)}$. The string $(1,0,n,n)$ corresponds to the quark $\psi^{(n)}$. Here, we show the strings up to $n\!=\!8$. In Fig.\ref{FirstPlots}A--F, some string junctions are constructed. For details, see Fig.\ref{closeup}.}
\label{FirstPlots}
\end{figure}%
Secondly we consider $\psi^{(1)}$. It corresponds to a string $(1,0,0,0)$ going around the 7-branes once anti-clockwisely. The string crosses the branch cuts in $\Real z\!>\!b+2c$. Then the charges are changed to $K_+K_-K_0{}^t\!(1,0,0,0)={}^t\!(1,0,1,1)$ as depicted in Fig.\ref{FirstPlots}A. Thus $\psi^{(1)}$ corresponds to a string $(1,0,1,1)$. The string sweeps a region in the first quadrant of the $z$-plane, as we increase $\phi$. Moreover, as depicted in Fig.\ref{FirstPlots}B--C, the string hits the 7-brane $[0,1]$ at $z\!=\!b+2c$ and becomes a string junction. The detailed configuration near the merging point of strings is shown in Fig.\ref{closeup}. The junction is constructed from three strings: $(1,-1,1,0)$ which comes from $(1,0,0,0)$ crossing the cuts between $z\!=\!0$ and $z\!=\!b-2c$, $(0,1,0,1)$ emanating from $[0,1]$ at $z\!=\!b+2c$, and the outgoing string $(1,0,1,1)$. As we increase $\phi$ further, the merging point draws a curve $C_1$ as shown in Fig.\ref{closeup}, and $(1,0,1,1)$ sweeps outside the region $S_1$ surrounded by $C_1$ and the real axis. Thus $\psi^{(1)}$ is stable outside $S_1$ in the moduli $u$-plane and disappears inside it. In addition, when the D3-brane is located on $C_1$, $(1,0,1,1)$ can decay into $(0,1,0,1)$ and $(1,-1,1,0)$. Thus $\psi^{(1)}$ becomes marginally stable when the moduli parameter $u$ is on $C_1$.
\begin{figure}[t]
\begin{center}
\includegraphics[bb=50 45 410 302,width=\textwidth,clip]{closeup.eps}
\end{center}
\caption{\footnotesize The enlarged illustrations of a string junction with the outgoing string $(1,0,1,1)$. We illustrate the point where the strings merge by a blob $\circ$.  Connecting these blobs, we get a curve stretched from the 7-brane at $z\!=\!b+2c\,(=\!6)$ to the one at $z\!=\!b-2c\,(=\!4)$. We call this curve $C_1$, the curve of marginal stability for $\psi^{(1)}$.}
\label{closeup}
\end{figure}%

Thirdly we consider $\psi^{(2)}$. It corresponds to $(1,0,2,2)$, which comes from a string $(1,0,1,1)$ going around the 7-branes once more (see Fig.\ref{FirstPlots}C--D). As depicted in Fig.\ref{FirstPlots}E, the string hits the 7-brane at $z\!=\!b+2c$ again and becomes a complicated string junction. As we increase $\phi$, the merging point of the strings draws a curve $C_2$, and $(1,0,2,2)$ sweeps outside the region $S_2$ surrounded by $C_2$ and the real axis. Thus $\psi^{(2)}$ is stable outside the region and disappears inside it. Note that the merging point is apparently under $C_1$. Consequently, $S_2$ is inside $S_1$, as shown in Fig.\ref{CMSs}.
\begin{figure}[t]
\begin{center}
\includegraphics[bb=50 50 425 260,width=\textwidth,clip]{CMSs.eps}
\end{center}
\caption{\footnotesize The marginal stability curves for $\psi^{(n)}$ ($1\leq n\leq7$). Here we also set $z\pm2c=6,4$.}
\label{CMSs}
\end{figure}%

On the basis of these observations, we next consider $\psi^{(n)}$ ($n\!\geq\!3$). In general, $\psi^{(n)}$ corresponds to a string $(1,0,n,n)$, which appears as $(1,0,n\!-\!1,n\!-\!1)$ crosses the branch cuts in $\mbox{Re}z\!>\!b+2c$. The string hits $[0,1]$ at $z\!=\!b+2c$ and an additional string $(0,1,0,1)$ is created. The merging point of the strings draws a curve $C_n$, which connects $z\!=\!b\pm 2c$ in the upper half $u$-plane, as we increase $\phi$. Simultaneously, $(1,0,n,n)$ sweeps outside the region $S_n$ surrounded by $C_n$ and the real axis. Thus $\psi^{(n)}$ appears outside $S_n$ and disappears inside it. The region $S_n$ is inside $S_{n-1}$ as shown in Fig.\ref{CMSs}. Therefore, $\psi^{(n)}$ disappears in numeric order of $n$ as we change the moduli parameter from a value above $C_1$ to the segment $[b-2c,b+2c]$. Similar analysis can be done for $\psi^{(n)}$ with negative $n$. It corresponds to a string $(1,0,0,0)$ going around the 7-branes $\abs{n}$ times clockwisely. One can derive the curve of marginal stability for $\psi^{(n)}$, and obtain the mirror image of that for $\psi^{(-n)}$ with respect to the real axis in the $u$-plane. These results are similar to the quark KK spectrum in the strong coupling limit $g_5\to\infty$ \cite{Ohtake3}.

\piccaptionoutside
\piccaption{\footnotesize The positions of two singularities at $z\!=\!b\pm2c$ depend on $g_5$. On the one hand, they collide in the limit of $g_5\to0$. On the other, the singularity $z\!=\!b-2c$ collides with the one at $z\!=\!0$ in the strong coupling limit, $g_5\to\infty$.\label{ccFig}}
\parpic[r]{\includegraphics[bb=50 45 260 198,width=200pt,clip]{ccFig.eps}}\picskip{15}
Now we determine the $g_5$ dependence of the quark KK spectrum. From \eqref{eqn:bf} and \eqref{eqn:cf}, we see that the positions of singularities, $z\!=\!b\pm 2c$, depend on $g_5$ as shown in Fig.\ref{ccFig}. The distance of the singularities becomes small as we decrease $g_5$. Then the curves of marginal stability, which connect the two singularities, also become small. As an example, we show the curve of $\psi^{(1)}$ for $g_5\!=\!3,4,5,6$ in Fig.\ref{BCflow}. The curve shrinks to a point in the limit $g_5\to 0$, where two singularities at $z\!=\!b\pm 2c$ collide. Therefore, the nonperturbative jumps of the quark KK spectrum disappear in this limit, as was expected from the perturbative analysis. On the other hand, in the limit $g_5\to\infty$, $z\!=\!b-2c$ coincides with $z\!=\!0$. Then the quark KK spectrum in the strong coupling limit is reproduced.
\begin{figure}[h]
\begin{center}
\includegraphics[bb=60 50 402 196,width=\textwidth]{BCflow.eps}
\end{center}
\caption{\footnotesize The marginal stability curve $C_1$ of $\psi^{(1)}$ for $g_5\!=\!3,4,5,6$. The weaker $g_5$ becomes, the shorter the curve $C_1$ becomes.}
\label{BCflow}
\end{figure}%

\paragraph*{$W$-bosons}
Next we are interested in $W_\mu^{(0)}$. It corresponds to a string $(1,0)$ emanating from the D3-brane, going around the 7-branes at $z\!=\!0$, and coming back to the D3-brane. The string crosses the branch cut from $z\!=\!0$ and becomes a string $(-1,0)$ because of the monodromy. Both the geodesic of $(1,0)$ and that of $(-1,0)$ are the same with that of $(1,0,0,0)$, a string corresponding to $\psi^{(0)}$. Therefore, the region where the geodesic for $W_\mu^{(0)}$ sweeps is the same with that for $\psi^{(0)}$. Then the stability of $W_\mu^{(0)}$ is the same with $\psi^{(0)}$; it is stable for all the moduli $u$-plane. In addition, a KK state $W_\mu^{(n)}$ corresponds to a string corresponding to $W_\mu^{(0)}$ which goes around the 7-branes $n$ times anti-clockwisely. The string has the same geodesic for $\psi^{(n)}$. Thus we conclude that $W_\mu^{(n)}$ is stable outside $S_n$ and disappears inside it.

\paragraph*{Unbroken $U(1)$ gauge bosons}
Before concluding this paper, we shall consider unbroken $U(1)$ gauge bosons. We start with $A_{\mu}^{(0)}$. It corresponds to a string $(1,0)$ localized on the D3-brane probe at $z\!=\!u$. Since the string appears for any value of $u$, $A_{\mu}^{(0)}$ is stable for all the $u$-plane.

Next we consider $A_{\mu}^{(1)}$. It corresponds to a string $(1,0)$ emanating from the D3-brane probe, going around all the 7-branes once anti-clockwisely, and coming back to the D3-brane. The geodesic equation is given by
\begin{equation}
\Arg\{a(z)-a(x)\} = 0,
\end{equation}
where $x$ is a point where the string passes through. The geodesics for various $x$ are loops as shown in Fig.\ref{SecondPlots}. As we decrease $x$ from $\infty$ to $b+2c$, the loop becomes small. When $x\!=\!b+2c$, the loop hits the 7-brane at $z\!=\!b+2c$ and becomes a string junction as depicted in Fig.\ref{SecondPlots}B. As we decrease $x$ from $b+2c$ to $b-2c$, the loop part of the junction collapses to a straight line as depicted in Fig.\ref{SecondPlots}C. In any case, when the D3-brane is located on the loop, the junction cannnot decay and is observed as a stable $A_{\mu}^{(1)}$. Since the loop sweeps all the $z$-plane but the segment between $z\!=\!0$ and $z\!=\!b+2c$, $A_\mu^{(1)}$ is stable for all the $u$-plane but the segment. On the other hand, when the D3-brane is located on the segment, the junction can decay into two parts.  Thus the segment is the marginal stability curve of $A_\mu^{(1)}$.
\begin{figure}[t]
\begin{center}
\begin{tabular}{ccc}
{\scriptsize A}\hspace{-1em}\includegraphics[bb=50 50 220 210,width=140pt,clip]{SecondPlot1.eps}&\hspace{-1.5em}
{\scriptsize B}\hspace{-1em}\includegraphics[bb=50 50 220 210,width=140pt,clip]{SecondPlot2.eps}&\hspace{-1.5em}
{\scriptsize C}\hspace{-1em}\includegraphics[bb=50 50 220 210,width=140pt,clip]{SecondPlot3.eps}\\
\end{tabular}
\end{center}
\caption{\footnotesize The string geodesics corresponding to the lightest gauge KK state $A_\mu^{(1)}$.}
\label{SecondPlots}
\end{figure}%

Finally, we consider $A_\mu^{(n)}$ ($n\!\!>\!\!1$). This corresponds to a string $(1,0)$ going around the 7-branes $n$ times. The string corresponds to $n$ loop strings or loop string junctions derived for $A_\mu^{(1)}$. Thus $A_\mu^{(n)}$ can decay into $n$ $A_\mu^{(1)}$ for any value of $u$. Similary, one can derive that $A_{\mu}^{(-1)}$ is stable for all the $u$-plane but the segment and $A_\mu^{(-n)}$ ($n\!\!>\!\!1$) can decay into $n$ $A_{\mu}^{(-1)}$.

\section*{Acknowledgements}
Y.~O. would like to thank A.~Sugamoto and  T.~Suzuki for useful discussions.

redpajama_set_name: RedPajamaArXiv


Forced Node Shutdown With Message: "The file system is full (File system full)"
Node failure with file system errors, such as "file system is full".
Increase in size of cluster data, logs, and/or addition of new files (backups etc). Or, failure to remove old, unused files.


W. Ammar, G. Mulcaire, M. Ballesteros, C. Dyer, and N. A. Smith, One parser, many languages. CoRR http, 2016.
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M. Artetxe, G. Labaka, and E. Agirre, Learning bilingual word embeddings with (almost) no bilingual data, Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp.451-462, 2017.
U. Barman, A. Das, J. Wagner, and J. Foster, Code Mixing: A Challenge for Language Identification in the Language of Social Media, Proceedings of the First Workshop on Computational Approaches to Code Switching, pp.13-23, 2014.
P. Bojanowski, E. Grave, A. Joulin, and T. Mikolov, Enriching word vectors with subword information, 2016.
K. Cho, Natural language understanding with distributed representation . arXiv preprint http, 2015.
T. Dozat, P. Qi, and C. D. Manning, Stanford's Graph-based Neural Dependency Parser at the CoNLL 2017 Shared Task, Proceedings of the CoNLL 2017 Shared Task: Multilingual Parsing from Raw Text to Universal Dependencies, pp.20-30, 2017.
C. Gerstenberger, N. Partanen, and M. Rießler, Instant annotations in ELAN corpora of spoken and written Komi, an endangered language of the Barents Sea region, Proceedings of the 2nd Workshop on the Use of Computational Methods in the Study of Endangered Languages, pp.57-66, 2017.
C. Gerstenberger, N. Partanen, M. Rießler, and J. Wilbur, Utilizing Language Technology in the Documentation of Endangered Uralic Languages, The Northern European Journal of Language Technology, vol.4, pp.29-47, 2016.
J. Guo, W. Che, D. Yarowsky, H. Wang, and T. Liu, Crosslingual dependency parsing based on distributed representations, Proceedings of ACL, 2015.
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K. Liu, Y. Lü, W. Jiang, and Q. Liu, Bilingually-guided monolingual dependency grammar induction, pp.1063-1072, 2013.
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Ideal for elegant dining presentations.
This delicate fish is loved for its mild taste & tender texture. It's bright-white, petite fillets are excellent for classy plate presentations and perfect for showing off colorful seafood sauces.
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text:
Q: Extracting words from non unique table rows Tableau 2020.2.6 I have a list of data in tableau with different total string count and different suffixes for example:

*

*SAO JOSE DO RIO PRETO 1

*SAO JOSE DO RIO PRETO 2

*SAN LUIS 1

*BELO HORIZONTE 3

*RIO DE JANEIRO EDU

*GOIANIA (Jc-01)

*RIO DE JANEIRO (JE-09)

*RIO DE JANEIRO 1 (CFMG)

In tableau 2020.2.6 ... REGEXP_EXTRACT(string, "^([A-Z]+ )*[A-Z]+") does not work.
Thank you in advance for your tips.

A: the following regular expression will match the city names
^(?:[A-Z][a-z]+ )*[A-Z][a-z]+

use it with REGEXP_EXTRACT(string, "^(?:[A-Z][a-z]+ )*[A-Z][a-z]+")

redpajama_set_name: RedPajamaStackExchange


The struggles that Chipotle has been dealing with lately are no secret; the Mexican fast food giant just can't seem to catch a break. But it turns out burrito bowl and taco lovers are the winners here: Chipotle is giving away 21 million more burritos in an effort to win back trust and love.
According to the Associated Press, Chipotle has done the unthinkable — it's suffered its first quarter of losses as a company. In an effort to boost lagging sales that might be related to health concerns (the chain was associated with a number of outbreaks late last year), the company is going to send out even more free burrito goodness into the universe in hopes of return good karma. It already did that on February 8th, giving away 5.3 million free burritos, but the company wants to go farther.
Check that mailbox: Chipotle is going to give away 21 million coupons for free burritos (or any entree) via direct mail — which is about one for every 12 Americans out there — valid for use at any of their 2,000 stores. That means free tacos, free bowls and free salads for all those who are lucky enough to get a coupon to help #makechipotlegreatagain and fill up the restaurants with new and returning customers.
Tweet us your favorite Chipotle hacks @BritandCo!


As a software engineer, I see the human mind as a beautiful combination of software and hardware. That's why I'm trying to hack my son's brain.
Caleb, 6, suffers from sensory processing disorder. To get a glimpse of what life is like for him, imagine you have no peripheral vision, and you constantly hear echos and distorted, out-of-sync sounds, making it hard to understand speech or appreciate music. When you walk, you can't tell where your legs are, or whether your arms are swinging. Sometimes just keeping your balance is difficult. You exasperate people for doing things you're not even aware of, like bumping into them or not making eye contact.
Like computers that can't multitask, or networks that lose information, this neurological disorder prevents the brain from correctly processing sensory input. The cause of SPD is a mystery, but the effects are very real.
Caleb is very bright, verbal, and a marvelous reader. But his brain can't handle all of the sensory input his body is sending him. His senses work individually to some extent, but when they are combined, his brain loses information.
The traditional treatment for SPD is occupational therapy. But I'm convinced that what Caleb needs instead is for his brain to be reprogrammed, recalibrated. With the help of some professionals and some surreal neurotechnology, we are trying to do just that.
The brain hack is a three-part "multisensory intervention program" at the Sensory Learning Center in Boulder, Colorado. A technician there subjects him to specialized light, sound, and motion therapy in a controlled environment. The goal is to help his brain reorganize the way it coordinates multisensory information. I have heard story after amazing story of children who have been helped by this program. It isn't cheap, and it isn't guaranteed, but I have to give my son a chance.
Many people with SPD don't process sound the way they should. Some frequencies sound too loud, too soft, or even delayed. Sometimes certain frequencies are even processed in the wrong hemisphere of the brain, a condition called auditory laterality. These conditions can make the perception of sound so confusing that some people suffering from it never learn how to talk.
Part of Caleb's hack is to retrain his brain to diminish over-sensitive frequencies and correct auditory laterality. Wearing headphones, he listens to music clips equalized to help his brain listen differently – without hot-spots, delays, or garbled information.
The treatment is based on the work of Dr. Guy Berard, a world-renowned hearing specialist who developed a program called Auditory Integration Training, which involves two 30-minute sessions daily for 10 consecutive days. The results, described in his book Hearing Equals Behavior, are encouraging.
Another problem common in SPD is a constricted field of vision. The brain doesn't process all of the information the eyes are seeing. This impacts everything from situational awareness to coordinating balance.
The second part of the hack involves intense colored lights tuned to precise frequencies. The colors create synaptic responses in different parts of the brain. During the treatment he is in a completely dark room, staring up at a pulsing colored light.
Other types of light therapy are commonly used to treat depression in adults and jaundice in children. This particular treatment is backed by research (.pdf) and has been highly successful in helping patients develop a widened field of vision and improved color reception. With these benefits often come better memory, learning, situational awareness, and even social skills.
Caleb also has a subset of SPD known as sensory-seeking. It is as though his ability to register motion, pressure, and even pain is significantly muted. As a result, he seeks out extra stimulation in any number of ways. He careens through life, often running into things and people with abandon.
To address these problems, the third modality in Caleb's treatment deals with the vestibular system, which is responsible for controlling your balance and posture.
While lying on a specially-designed motion table, he listens to the special headphones and looks at the colored lights. The table mimics the motion of a ferris wheel, proceeding in a circle either along the anterior-posterior axis (head to toe), or from side to side.
Anecdotal evidence (.pdf - via the internet archive) shows that this multi-sensory integration approach, done in a controlled manner, helps the brain coordinate and permanently connect sensory inputs more effectively then when they are exercised alone.
As I write, Caleb is in his last day of treatment at the Center. This afternoon the first phase will be complete, and tomorrow we will administer only the light therapy at home for another 18 days. Over the weeks and months to come, we should start to notice improvements in his movement, his behavior, and even his relationships.
That is, of course, if the hack works.