On the baryon-color-flavor (BCF) anomaly in vector-like theories

TL;DR

This paper investigates the BCF 't Hooft anomaly in vector-like theories with fractional flux backgrounds, deriving constraints on IR dynamics and revealing a link between anomaly conditions and phase transitions related to the $ heta$-angle.

Contribution

It introduces the concept of BCF anomaly in vector-like theories and establishes new constraints on their IR behavior, especially regarding composite fermions and $ heta$-angle periodicity.

Findings

BCF anomaly constrains IR composite fermion formation.

Conditions for anomaly lead to $ heta$-angle phase transitions.

Massive theories exhibit $ heta$-periodicity anomalies.

Abstract

We consider the most general fractional background fluxes in the color, flavor, and baryon number directions, compatible with the faithful action of the global symmetry of a given theory. We call the obstruction to gauging symmetries revealed by such backgrounds the baryon-color-flavor (BCF) 't Hooft anomaly. We apply the BCF anomaly to vector-like theories, with fermions in higher-dimensional representations of arbitrary N-ality, and derive non-trivial constraints on their IR dynamics. In particular, this class of theories enjoys an independent discrete chiral symmetry and one may ask about the fate of this symmetry in the background of BCF fluxes. We show that, under certain conditions, an anomaly between the chiral symmetry and the BCF background rules out massless composite fermions as the sole player in the IR: either the composites do not form or additional contributions to the matching of the BCF anomaly are required. We can also give a flavor-symmetric mass to the fermions, smaller than or of order the strong scale of the theory, and examine the $\theta$-angle periodicity of the theory in the BCF background. Interestingly, we find that the conditions that rule out the composites are the exact same conditions that lead to an anomaly of the $\theta$ periodicity: the massive theory will experience a phase transition as we vary $\theta$ from $0$ to $2\pi$.