Dashen's Phenomenon in Gauge Theories with Spontaneously Broken Chiral Symmetries

TL;DR

This paper investigates Dashen's phenomenon within the Leutwyler--Smilga regime of QCD, deriving relations between chiral condensate and topological density, and analyzing the zeros of partition functions to understand the phenomenon.

Contribution

It provides new analytical expressions for chiral condensate and topological density in QCD with various gauge groups and quark representations, clarifying the mechanism of Dashen's phenomenon.

Findings

Derived simple expressions for chiral condensate and topological density.

Established the relationship between condensate and topological density.

Analyzed partition function zeros to elucidate Dashen's phenomenon.

Abstract

We examine Dashen's phenomenon in the Leutwyler--Smilga regime of QCD with any number of colors and quarks in either the fundamental or adjoint representations of the gauge group. In this limit, the theories only depend on simple combinations of quark masses, volume, chiral condensate and vacuum angle. Based upon this observation, we derive simple expressions for the chiral condensate and the topological density and show that they are in fact related. By examining the zeros of the various partition functions, we elucidate the mechanism leading to Dashen's phenomena in QCD.