Schur correlation functions on S 3 × S 1

Abstract

Abstract The Schur limit of the superconformal index of four-dimensional N $$ \mathcal{N} $$ = 2 superconformal field theories has been shown to equal the supercharacter of the vacuum module of their associated chiral algebra. Applying localization techniques to the theory suitably put on S 3 × S 1, we obtain a direct derivation of this fact. We also show that the localization computation can be extended to calculate correlation functions of a subset of local operators, namely of the so-called Schur operators. Such correlators correspond to insertions of chiral algebra fields in the trace-formula computing the supercharacter. As a by-product of our analysis, we show that the standard lore in the localization literature stating that only off-shell supersymmetrically closed observables are amenable to localization, is incomplete, and we demonstrate how insertions of fermionic operators can be incorporated in the computation.

Keywords

• Supersymmetric Gauge Theory
• Conformal Field Theory
• Extended Supersymmetry
• Supersymmetry and Duality