On Instantons at Large Charge

TL;DR

This paper investigates the behavior of two-point functions of chiral primary operators at large R-charge in N=2 superconformal field theories, using supersymmetric localization to analyze instanton effects and their universality.

Contribution

It provides an analytic test of the universal large-charge behavior in SU(2) SQCD with four flavors, emphasizing the role of instantons and the interplay between weak-coupling and large-charge expansions.

Findings

Large R-charge correlators are independent of gauge coupling in SU(2) SQCD.

Instantons significantly influence the large-charge regime.

Results have implications for Argyres-Douglas theories.

Abstract

The large R-charge limit of two-point functions of chiral primary operators in rank-one N=2 superconformal field theories exhibits a universal behavior controlled by the effective field theory on their Coulomb branch. In the case of SU(2) SQCD with four flavors, this behavior is expected to be independent of the exactly-marginal gauge coupling. We provide an analytic test of this prediction by computing the correlators directly via supersymmetric localization. Our analysis clarifies the interplay between the weak-coupling expansion and the large-charge expansion, with special emphasis on the precise role played by gauge-theory instantons in the latter regime. We conclude with remarks on the implications of our results for analogous observables in Argyres-Douglas theories.