  Dynamics and symmetry realization in various chiral gauge theories in four
dimensions are investigated, generalizing a recent work by M. Shifman and the
present authors, by relying on the standard 't Hooft anomaly matching
conditions and on some other general ideas. These requirements are so strong
that the dynamics of the systems are severely constrained. Color-flavor or
color-flavor-flavor locking, dynamical Abelianization, and combinations of
these, are powerful ideas which often leads to solutions of the anomaly
matching conditions. Moreover, a conjecture is made on generation of a mass
hierarchy associated with symmetry breaking in chiral gauge theories, which has
no analogues in vector-like gauge theories such as QCD.

High Energy Physics - Theory;High Energy Physics - Lattice;High Energy Physics - Phenomenology