Dynamical Abelianization and anomalies in chiral gauge theories

Abstract

We explore the idea that in some class of strongly-coupled chiral SU(N) gauge theories the infrared dynamics might be characterized by a bifermion condensate in the ad- joint representation of the color gauge group. As an illustration, in this work we revisit an SU(N) chiral gauge theory with Weyl fermions in a symmetric (ψ) and anti-antisymmetric (χ) tensor representations, together with eight fermions in the anti-fundamental representations (η), which we called ψχη model in the previous investigations. We study the infrared dynamics of this system more carefully, by assuming dynamical Abelianization, a phenomenon familiar from \U0001d4a9 = 2 supersymmetric gauge theories, and by analyzing the way various continuous and discrete symmetries are realized at low energies. We submit then these ideas to a more stringent test, by taking into account some higher-form symmetries and the consequent mixed anomalies. A detailed analysis of the mixed anomalies involving certain 0-form U(1) symmetries and the color-flavor locked 1-form ℤN symmetry in the ψχη system shows that the proposed infrared dynamics is consistent with it.