Magnetic discrete gauge field in the confining vacua and the supersymmetric index

TL;DR

This paper provides evidence that confining vacua in Yang-Mills theories include magnetic discrete gauge fields by matching supersymmetric indices in ultraviolet and infrared regimes.

Contribution

It introduces a new calculation of the supersymmetric index to support the presence of magnetic z gauge fields in confining vacua.

Findings

Supersymmetric index matches in UV and IR regimes.

Supports the existence of magnetic z gauge fields in confining vacua.

Provides evidence for topological degrees of freedom in Yang-Mills theory.

Abstract

It has recently been argued that the confining vacua of Yang-Mills theory in the far infrared can have topological degrees of freedom given by magnetic $\mathbb{Z}_q$ gauge field, both in the non-supersymmetric case and in the N=1 supersymmetric case. In this short note we give another piece of evidence by computing and matching the supersymmetric index of the pure super Yang-Mills theory both in the ultraviolet and in the infrared.