7D supersymmetric Yang-Mills on curved manifolds

Authors: Konstantina Polydorou, Andreas Rocén and Maxim Zabzine

Preprint Number: UUITP-36/17

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 discuss briefly the case of 3-Sasaki manifolds and suggest the plausible form of the full non-perturbative answer.