Condensates and anomaly cascade in vector-like theories

A bstract We study the bilinear and higher-order fermion condensates in 4-dimensional SU( N ) gauge theories with a single Dirac general representation. Augmented mixed anomaly between 0-form discrete chiral, 1-form center, baryon number symmetries (BC anomaly), we sort out that admit vanishing bilinears. Then, BC is utilized to prove, absence of topological quantum field theory, nonvanishing bilinears are inevitable infrared-gapped 2-index (anti)symmetric fermions. also contrast anomalies show it former determines infrared physics; argue lurks deep while just variations local terms. provide evidence this assertion by studying vector-like compactified on small spacial circle. These weakly-coupled, under analytical control, they dual description terms abelian photons determine dynamics. talk directly center symmetry order match anomaly, matched fiat. Finally, fate when held at finite temperature. The effective theory describes low-energy physics 2-dimensional. cascades from 4 2 dimensions.