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

A review of the T N theory and its cousins

The theory is a four-dimensional superconformal field theory that has played a central role in the analysis of supersymmetric dualities in the last few years. The aim of this review is to collect known properties of the theory and its cousins in one place as a quick reference

On skein relations in class S theories

Loop operators of a class S theory arise from networks on the corresponding Riemann surface, and their operator product expansions are given in terms of the skein relations, that we describe in detail in the case of class S theories of type A. As two applications, we explicitly determine networks corresponding to dyonic loops of N = 4 S U 3 $$\mathcal{N}=4\;\mathrm{S}\mathrm{U}(3)$$ super Yang-Mills, and compute the superconformal index of a nontrivial network operator of the T 3 theory