Aₖ F Chiral Gauge Theories

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We study asymptotically free chiral gauge theories with an SU(N) gauge group and chiral fermions transforming according to the antisymmetric rank-k tensor representation, Aₖ ≡ [k]ₙ, and the requisite number, n F, of copies of fermions in the conjugate fundamental representation, F ≡ [1]ₙ, to render the theories anomaly-free. We denote these as Aₖ F theories. We take N ≥ 2k+1 so that n F ≥ 1. The A₂ F theories form an infinite family with N ≥ 5, but we show that the A₃ F and A₄ F theories are only asymptotically free for N in the respective ranges 7 ≤ N ≤ 17 and 9 ≤ N ≤ 11, and that there are no asymptotically free Aₖ F theories with k ≥ 5. We investigate the types of ultraviolet to infrared evolution for these Aₖ F theories and find that, depending on k and N, they may lead to a non-Abelian Coulomb phase, or may involve confinement with massless gauge-singlet composite fermions, bilinear fermion condensation with dynamical gauge and global symmetry breaking, or formation of multifermion condensates that preserve the gauge symmetry. We also show that there are no asymptotically free, anomaly-free SU(N) Sₖ F chiral gauge theories with k ≥ 3, where Sₖ denotes the rank-k symmetric representation.