2D BPS Rings from Sphere Partition Functions

TL;DR

This paper develops a method to compute extremal BPS correlators in 2D N=(2,2) theories using sphere partition functions, addressing operator mixing issues and illustrating with models like the Quintic GLSM.

Contribution

It introduces a localization-based approach to calculate extremal correlators involving BPS operators in 2D supersymmetric theories, resolving operator mixing complications.

Findings

Derived explicit formulas for BPS correlators from sphere partition functions.

Applied the method to the Quintic GLSM and Landau-Ginzburg models.

Clarified the impact of conformal anomaly on correlator computations.

Abstract

We consider extremal correlation functions, involving arbitrary number of BPS (chiral or twisted chiral) operators and exactly one anti-BPS operator in 2D N=(2,2) theories. These correlators define the structure constants in the rings generated by the BPS operators with their operator product expansions. We present a way of computing these correlators from the sphere partition function of a deformed theory using localization. Relating flat space and sphere correlators is nontrivial due to operator mixing on the sphere induced by conformal anomaly. We discuss the supergravitational source of this complication and a resolution thereof. Finally, we demonstrate the process for the Quintic GLSM and the Landau-Ginzburg minimal models.