Spontaneous symmetry breaking in pure 2D Yang-Mills theory

Abstract

We consider purely topological 2D Yang-Mills theory on a torus with the second Stiefel-Whitney class added to the Lagrangian in the form of a θ term. It will be shown that at θ=π there exists a class of SU(2N)/Z2 (N>1) gauge theories with a twofold degenerate vacuum, which spontaneously breaks the time reversal and charge conjugation symmetries. The corresponding order parameter is given by the generator O of the ZN one-form symmetry.