Spontaneous symmetry breaking in pure 2D Yang-Mills theory

TL;DR

This paper investigates how adding a $ heta$-term to pure 2D Yang-Mills theory on a torus leads to spontaneous symmetry breaking at $ heta=\pi$, revealing degenerate vacua and symmetry-breaking order parameters.

Contribution

It demonstrates the existence of spontaneous symmetry breaking and degenerate vacua in pure 2D Yang-Mills theory with a $ heta$-term at $ heta=\pi$, a novel insight in topological gauge theories.

Findings

Degenerate vacua at $ heta=\pi$ in certain gauge theories.

Spontaneous breaking of time reversal and charge conjugation symmetries.

Identification of the order parameter as the generator of $bZ_N$ one-form symmetry.

Abstract

We consider purely topological $2$d Yang-Mills theory on a torus with the second Stiefel-Whitney class added to the Lagrangian in the form of a $\theta$-term. It will be shown, that at $\theta=\pi$ there exists a class of $SU(2 N)/\mathbb{Z}_2$ ($N>1$) gauge theories with a two-fold degenerate vacuum, which spontaneously breaks the time reversal and charge conjugation symmetries. The corresponding order parameter is given by the generator $\mathcal{O}$ of the $\mathbb{Z}_N$ one-form symmetry.