On phases of 4d $Spin/SO$ Yang-Mills theories

Abstract

We study the low-temperature phase diagrams of $Spin(N)/SO(N{)}_{\pm }$ Yang-Mills theories as functions of the $\theta$-parameter. In particular, for every even integer $N\ge 4$, we find a phase diagram consistent with the center/CP mixed anomaly, via the technique of mixed gauge theory. The resulting phase diagrams are in perfect agreement with the phase diagrams of $Spin(N)/SO(N{)}_{\pm }$ super Yang-Mills theory softly broken by a small gaugino mass. In the case of $Spin(4k)$ Yang-Mills for an integer $k\ge 2$, only two phases appear in the phase diagram, while in the $Spin(4)$ case the phase diagram contains four SPT phases protected by the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ center symmetry. In the case of $Spin(4k+2)$ Yang-Mills for a positive integer $k$, the phase diagram contains four SPT phases protected by the ${\mathbb{Z}}_4$ center symmetry.

arXiv comment43 pages, 14 tables, 12 figures