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

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 ℤ q $$ {\mathbb{Z}}_q $$ gauge field, both in the non-supersymmetric case and in the N = 1 $$ \mathcal{N}=1 $$ 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