Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions

TL;DR

This paper classifies maximally supersymmetric backgrounds in ten-dimensional conformal supergravity, explores their symmetries, and constructs supersymmetric Yang-Mills theories on these backgrounds, revealing similarities with eleven-dimensional supergravity.

Contribution

It provides a comprehensive classification of supersymmetric backgrounds and demonstrates how to formulate Yang-Mills theory with rigid supersymmetry on them, extending previous understanding.

Findings

Classification of maximally supersymmetric backgrounds

Determination of their conformal symmetry superalgebras

Construction of supersymmetric Yang-Mills theories on these backgrounds

Abstract

We consider bosonic supersymmetric backgrounds of ten-dimensional conformal supergravity. Up to local conformal isometry, we classify the maximally supersymmetric backgrounds, determine their conformal symmetry superalgebras and show how they arise as near-horizon geometries of certain half-BPS backgrounds or as a plane-wave limit thereof. We then show how to define Yang-Mills theory with rigid supersymmetry on any supersymmetric conformal supergravity background and, in particular, on the maximally supersymmetric backgrounds. We conclude by commenting on a striking resemblance between the supersymmetric backgrounds of ten-dimensional conformal supergravity and those of eleven-dimensional Poincar\'e supergravity.