$\mathcal{N} = 2$ Schur index and line operators

Abstract: 4d $\mathcal{N} = 2$ SCFTs and their invariants can be often enriched by non-local BPS operators. In this paper we study the flavored Schur index of several types of N = 2 SCFTs with and without line operators, using a series of new integration formula of elliptic functions and Eisenstein series. We demonstrate how to evaluate analytically the Schur index for a series of $A_2$ class-$\mathcal{S}$ theories and the $\mathcal{N} = 4$ SO(7) theory. For all $A_1$ class-$\mathcal{S}$ theories we obtain closed-form expressions for SU(2) Wilson line index, and 't Hooft line index in some simple cases. We also observe the relation between the line operator index with the characters of the associated chiral algebras. Wilson line index for some other low rank gauge theories are also studied.