Supersymmetric sigma models and the 't Hooft instantons

TL;DR

This paper explores supersymmetric sigma models related to instantons, extending Witten's model to include more supersymmetry and specific geometric backgrounds, leading to explicit 't Hooft instanton solutions.

Contribution

It introduces generalized models with enhanced supersymmetry and explicit geometric conditions, connecting sigma models to 't Hooft instantons in four dimensions.

Findings

Extended supersymmetric sigma models with (4,4) invariance.

Explicit construction of 't Hooft instantons via scalar functions.

Geometric background characterized by Laplace's equation.

Abstract

Witten's linear sigma model for ADHM instantons possesses a natural $(0,4)$ supersymmetry. We study generalizations of the infrared limit of the model that are invariant under $(4,4)$ supersymmetry. In the case of four space-time dimensions a background with a conformally flat metric and torsion is required. The geometry is specified by a single real scalar function satisfying Laplace's equation. It gives rise to 't Hooft instantons for the gauge group $SU(2)$, instead of the general ADHM instantons for an $SO(n)$ gauge group in the case $(0,4)$.