content_image/317838.jpg content_image/317844.jpg
solution is 

<img src='content_image/317838.jpg'>

<img src='content_image/317844.jpg'>

with φ = arccos( B $^{2}$− i 2 / $^{3}$( − $_{1+}$√$_{3)}$$_{r}$ 2 B $^{2}$+ i 2 / 3 $_{(1+}$√$_{3)}$$_{r}$ 2 ). F ( φ, m ) is the incomplete elliptic integral of the first kind, using the convention defined in Mathematica version 5.2. 

The function is complex unless B = 0, meaning that the only well- behaved solution is when u$_{5}$ is equal to a constant. This is the solution with a zero valued condensate. By allowing m ̸ = 0 we have clearly broken the U(1) chiral symmetry that existed before. We showed in section 1.2.8 that QCD breaks chiral symmetry both by the spontaneous formation of a chiral condensate, and to a lesser extent, by the mass of the quarks. In this pure AdS system, the only way we can break chiral symmetry is by making the quarks massive. 

