7D supersymmetric Yang-Mills on curved manifolds

TL;DR

This paper explores 7D supersymmetric Yang-Mills theory on curved manifolds with Killing spinors, deriving explicit perturbative partition functions for certain geometries and proposing forms for non-perturbative contributions.

Contribution

It develops a cohomological reformulation of 7D SYM on Sasaki-Einstein manifolds and provides explicit perturbative partition functions for toric cases.

Findings

Derived explicit perturbative partition functions for toric Sasaki-Einstein manifolds.

Proposed a form for the full non-perturbative partition function.

Extended the cohomological approach to 7D SYM on K-contact manifolds.

Abstract

We study 7D maximally supersymmetric Yang-Mills theory on curved manifolds that admit Killing spinors. If the manifold admits at least two Killing spinors (Sasaki-Einstein manifolds) we are able to rewrite the supersymmetric theory in terms of a cohomological complex. In principle this cohomological complex makes sense for any K-contact manifold. For the case of toric Sasaki-Einstein manifolds we derive explicitly the perturbative part of the partition function and speculate about the non-perturbative part. We also briefly discuss the case of 3-Sasaki manifolds and suggest a plausible form for the full non-perturbative answer.