7D supersymmetric Yang-Mills on a 3-Sasakian manifold

Abstract

In this paper we study 7D maximally supersymmetric Yang-Mills on a specific 3-Sasakian manifold that is the total space of an $SO(3)$-bundle over $\mathbb{C}{P}^2$. The novelty of this example is that the manifold is not a toric Sasaki-Einstein manifold. The hyperkähler cone of this manifold is a Swann bundle with hypertoric symmetry and this allows us to calculate the perturbative part of the partition function of the theory. The result is also verified by an index calculation. We also discuss a factorisation of this result and compare it with analogous results for $S^7$.

39 pages, 9 figures, published version

References in corpus (4)

• Sasaki-Einstein Manifolds and Volume Minimisation
• Boundaries, Mirror Symmetry, and Symplectic Duality in 3d $\mathcal{N}=4$ Gauge Theory
• Gluing Nekrasov partition functions
• 7D supersymmetric Yang-Mills on curved manifolds

Cited by in corpus (5)

• SYM on Quotients of Spheres and Complex Projective Spaces
• Supersymmetric gauge theory on curved 7-branes
• From 5d Flat Connections to 4d Fluxes (the Art of Slicing the Cone)
• 7D supersymmetric Yang-Mills on hypertoric 3-Sasakian manifolds
• Five-dimensional cohomological localization and squashed $q$-deformations of two-dimensional Yang-Mills theory