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

TL;DR

This paper computes the perturbative partition function of 7D maximally supersymmetric Yang-Mills theory on a non-toric 3-Sasakian manifold, revealing new geometric insights and comparing with known results on $S^7$.

Contribution

It introduces a novel 3-Sasakian manifold not previously studied in this context and calculates its partition function using hypertoric symmetry techniques.

Findings

Partition function computed explicitly for the 3-Sasakian manifold.

Verification of results through index calculation.

Comparison with $S^7$ results shows similarities and differences.

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 hyperk\"ahler 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 $S^7$.