The resurgence of errors in the localization of $\mathcal{N} = 2$ superconformal Yang-Mills

TL;DR

This paper provides a physical interpretation of the analytic continuation of the partition function for superconformal SU(2) N=2 gauge theory, linking 4d complex saddles to 2d unstable instantons through a chiral algebra approach.

Contribution

It introduces a novel 2d construction that associates unstable instantons to 4d saddles, enhancing understanding of localization and analytic continuation in superconformal gauge theories.

Findings

Identifies 2d unstable instantons as counterparts to 4d complex saddles.

Connects chiral algebra subsector with Higgs branch localization.

Provides a physical interpretation for analytic continuation of the partition function.

Abstract

We give a physical interpretation for the analytic continuation of the partition function of superconformal SU$(2)$ $\mathcal{N}=2$ gauge theory on the four-sphere to all values of the Yang-Mills coupling. We show that a well-motivated 2d construction associates two-dimensional unstable instantons to the 4d complex saddles which appear as singularities in the integrand of the supersymmetric localization expression. The construction is based on the chiral algebra subsector, and aligns with the alternative Higgs branch localization.