<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math> Schur index and line operators
Zhaoting Guo, Yutong Li, Yiwen Pan, Yufan Wang
Abstract
4D $\mathcal{N}=2$ superconformal field theories and their invariants can be often enriched by nonlocal Bogomol'nyi-Prasad-Sommerfield operators. In this paper we study the flavored Schur index of several types of $\mathcal{N}=2$ superconformal field theories 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. The Wilson line index for some other low rank gauge theories is also studied.