Renormalization-group evolution and nonperturbative behavior of chiral gauge theories with fermions in higher-dimensional representations

We study the ultraviolet to infrared evolution and nonperturbative behavior of a simple set of asymptotically free chiral gauge theories with an SU(N) gauge group and an anomaly-free set of nSk copies of chiral fermions transforming as the symmetric rank-k tensor representation, Sk, and nA¯ℓ copies of fermions transforming according to the conjugate antisymmetric rank-ℓ tensor representation, A¯ℓ, of this group with k, ℓ≥2. As part of our study, we prove a general theorem guaranteeing that a low-energy effective theory resulting from the dynamical breaking of an anomaly-free chiral gauge theory is also anomaly-free. We analyze the theories with k=ℓ=2 in detail and show that there are only a finite number of these. Depending on the specific theory, the ultraviolet to infrared evolution may lead to a non-Abelian Coulomb phase, or may involve confinement with massless composite fermions, or fermion condensation with dynamical gauge and global symmetry breaking. We show that SkA¯k chiral gauge theories with k≥3 are not asymptotically free. We also analyze theories with fermions in Sk and A¯ℓ representations of SU(N) with k≠ℓ and k, ℓ≥2.