Supersymmetric Deformations of Maximally Supersymmetric Gauge Theories

TL;DR

This paper classifies all infinitesimal supersymmetric deformations of ten-dimensional super Yang-Mills theory and its reductions, using advanced algebraic methods like L-infinity and A-infinity algebras.

Contribution

It provides a complete description of all infinitesimal super Poincaré invariant deformations of these theories using homological algebra techniques.

Findings

Classified all infinitesimal supersymmetric deformations.

Extended some deformations to formal deformations.

Developed algebraic tools for deformation analysis.

Abstract

We study supersymmetric and super Poincar\'e invariant deformations of ten-dimensional super Yang-Mills theory and of its dimensional reductions. We describe all infinitesimal super Poincar\'e invariant deformations of equations of motion of ten-dimensional super Yang-Mills theory and its reduction to a point; we discuss the extension of them to formal deformations. Our methods are based on homological algebra, in particular, on the theory of L-infinity and A-infinity algebras. The exposition of this theory as well as of some basic facts about Lie algebra homology and Hochschild homology is given in appendices.