  We study the dynamics of $SU(N)$ chiral gauge theories with massless fermions
belonging to various combinations of the symmetric, antisymmetric or
fundamental representations. We limit ourselves to the gauge-anomaly-free and
asymptotically free systems. 't Hooft anomaly-matching conditions severely
limit the possible RG flows. In vectorlike theories such as the quantum
chromodynamics, gauge-invariant ``quark-antiquark" condensates form and
characterize the IR dynamics, and the anomaly matching involves the
Nambu-Goldstone bosons. In some other special cases, such as the
Bars-Yankielowicz (BY) or Georgi-Glashow (GG) models, a hypothetical solution
was proposed in the literature, with no global symmetry breaking and with some
simple set of composite massless fermions saturating all the anomalies. For the
BY and GG systems, actually, a more plausible candidate for their IR physics is
the dynamical Higgs phase, with a few simple bi-fermion color-flavor locked
condensates, breaking the color and flavor symmetries, partially or totally.
Remarkably, the 't Hooft anomaly-matching (and generalized anomaly-matching)
conditions are automatically satisfied in this phase. Another interesting
possibility, occurring in some chiral gauge theories, is dynamical
Abelianization, familiar from ${\cal N}=2$ supersymmetric gauge theories. We
explore here even more general types of possible IR phases than the ones
mentioned above, for wider classes of models. With the help of large-N
arguments we look for IR free theories, whereas the MAC (maximal attractive
channel) criterion might suggest some simple bi-fermion condensates
characterizing the IR dynamics of the systems. In many cases the low-energy
effective theories are found to be described by quiver-like gauge theories,
some of the (nonAbelian) gauge groups are infrared-free while some others might
be asymptotically free.
