Generalized instantons in N = 4 super Yang-Mills theory and spinorial geometry

TL;DR

This paper classifies supersymmetric solutions in Euclidean N=4 super Yang-Mills theory using spinorial geometry, revealing generalized instantons with scalar fields and connections to Hitchin and octonionic instanton equations.

Contribution

It introduces a classification of generalized instantons with scalar fields in N=4 super Yang-Mills, linking them to Hitchin, Donaldson, and octonionic instanton equations via dimensional reduction.

Findings

Classified supersymmetric solutions using spinorial geometry.

Identified constraints similar to Hitchin equations.

Connected solutions to octonionic instanton equations.

Abstract

Using spinorial geometry techniques, we classify the supersymmetric solutions of euclidean ${\cal N}=4$ super Yang-Mills theory. These backgrounds represent generalizations of instantons with nontrivial scalar fields turned on, and satisfy some constraints that bear a similarity with the Hitchin equations, and contain the Donaldson equations as a special subcase. It turns out that these constraints can be obtained by dimensional reduction of the octonionic instanton equations, and may be rephrased in terms of a selfduality-like condition for a complex connection. We also show that the supersymmetry conditions imply the equations of motion only partially.