The Geometry of SUSY Enhancement

TL;DR

This paper offers a geometric framework explaining supersymmetry enhancement in 4D field theories via hyperk"ahler structures on Hitchin moduli spaces, providing new insights into IR physics without a-maximization.

Contribution

It introduces a geometric perspective on SUSY enhancement using Hitchin systems and derives IR Seiberg-Witten data without a-maximization, applicable to arbitrary rank theories.

Findings

Formulated a necessary algebraic condition for SUSY enhancement.

Derived IR Seiberg-Witten geometry for enhanced theories.

Provided Coulomb-branch operator dimensions without a-maximization.

Abstract

We provide a precise geometric picture that demystifies the phenomenon of supersymmetry enhancement along certain RG flows of four-dimensional field theories, recently discovered by Maruyoshi and Song. It applies to theories of arbitrary rank and it is based on a hyperk\"ahler-structure restoration on the moduli space of solutions of (twisted) Hitchin systems, which underly the class-S construction we use as an engineering tool. Along the way, we formulate a necessary algebraic condition for supersymmetry enhancement, and, when enhancement occurs, we are able to derive the Seiberg-Witten geometry and all conformal dimensions of Coulomb-branch operators for the infrared theory, without using a-maximization.