Supersymmetric gauge theories on five-manifolds

TL;DR

This paper develops a systematic method to construct and classify five-dimensional supersymmetric gauge theories on curved manifolds using holography, revealing geometric structures that ensure supersymmetry.

Contribution

It introduces a holographic approach to classify supersymmetric backgrounds on five-manifolds and constructs supersymmetric Lagrangians for gauge theories on these backgrounds.

Findings

Classification of supersymmetric five-manifolds with gravity duals

Identification of conformal Killing vectors and foliation structures

Construction of supersymmetric gauge theories on these backgrounds

Abstract

We construct rigid supersymmetric gauge theories on Riemannian five-manifolds. We follow a holographic approach, realizing the manifold as the conformal boundary of a six-dimensional bulk supergravity solution. This leads to a systematic classification of five-dimensional supersymmetric backgrounds with gravity duals. We show that the background metric is furnished with a conformal Killing vector, which generates a transversely holomorphic foliation with a transverse Hermitian structure. Moreover, we prove that any such metric defines a supersymmetric background. Finally, we construct supersymmetric Lagrangians for gauge theories coupled to arbitrary matter on such backgrounds.