7D supersymmetric Yang-Mills on curved 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.

arXiv comment49 pages, published version

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Cited by in corpus (10)

• Supersymmetric localization of refined chiral multiplets on topologically twisted $H^2\times S^1$
• SYM on Quotients of Spheres and Complex Projective Spaces
• A foliated Hitchin-Kobayashi correspondence
• Cohomological Localization of $\mathcal{N}=2$ Gauge Theories with Matter
• 7D supersymmetric Yang-Mills on a 3-Sasakian manifold
• 7D supersymmetric Yang-Mills on hypertoric 3-Sasakian manifolds
• From 5d Flat Connections to 4d Fluxes (the Art of Slicing the Cone)
• Supersymmetric gauge theory on curved 7-branes
• Five-dimensional cohomological localization and squashed $q$-deformations of two-dimensional Yang-Mills theory
• Seven-dimensional super Yang-Mills at negative coupling