Phase structure of linear quiver gauge theories from anomaly matching

TL;DR

This paper investigates the phase structure of linear quiver gauge theories using anomaly matching, revealing different symmetry behaviors depending on the quiver length and analyzing finite temperature effects.

Contribution

It provides a detailed analysis of anomaly matching conditions in linear quiver gauge theories for both even and odd quiver lengths, including finite temperature considerations.

Findings

For even K, symmetry breaking similar to QCD is expected.

For odd K, the anomaly is matched by massless composite fermions.

Finite temperature analysis relates critical temperatures to confinement and symmetry breaking.

Abstract

We consider the phase structure of the linear quiver gauge theory, using the 't Hooft anomaly matching condition. This theory is characterized by the length $K$ of the quiver diagram. When $K$ is even, the symmetry and its anomaly are the same as those of massless QCD. Therefore, one can expect that the spontaneous symmetry breaking similar to the chiral symmetry breaking occurs. On the other hand, when $K$ is odd, the anomaly matching condition is satisfied by the massless composite fermions. We also consider the thermal partition function under the twisted boundary conditions. When $K$ is even, from the anomaly at finite temperature, we estimate the relation between the critical temperatures associated with the confinement/deconfinement and the breaking of the global symmetry. Finally we discuss the anomaly matching at finite temperature when $K$ is odd.