Spontaneous symmetry breaking in pure 2D Yang-Mills theory

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 $SU(2N)/{\mathbb{Z}}_2$ ($N>1$) 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.

The ambiguity between the second Stiefel-Whitney class $w_2$ and an invariant of $PSU(N)$ bundles $u_2$ was removed. Conclusion section and more references were added in version 3