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Dynamical Abelianization and anomalies in chiral gauge theories

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 adjoint 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 ${\cal N}=2$ 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 $Z_N$ symmetry in the $ψχη$ system shows that the proposed infrared dynamics is consistent with it.