Four Dimensional Superconformal Index from $q$-Deformed Two Dimensional Yang-Mills Theory

We show that the superconformal index (the partition function on the three-sphere times a circle) of a certain class of 4D supersymmetric field theories is exactly equal to a partition function of $q$-deformed nonsupersymmetric 2D Yang-Mills theory.

Figure 1

An example of the rule to associate flavor fugacities for a nonmaximal puncture. Illustrated here is a puncture for $N=26$ with flavor symmetry $S\mathbf{(}U(3)U(2{)}^{2}U(1)\mathbf{)}$. The $S(\dots )$ constraint imposes $(ab{)}^5(cde{)}^4{f}^{2}gh=1$.