5D Super Yang-Mills on $Y^{p,q}$ Sasaki-Einstein manifolds

TL;DR

This paper develops a localization-based method to compute the partition function of 5D super Yang-Mills theories on $Y^{p,q}$ Sasaki-Einstein manifolds, revealing an $N^3$ scaling in the large N limit.

Contribution

It introduces a new special function generalizing the triple sine function and applies localization to compute the full perturbative partition function on $Y^{p,q}$ manifolds.

Findings

Derived the full perturbative partition function using localization.

Expressed the result in terms of a novel special function.

Found $N^3$ scaling for large N with a hypermultiplet in the adjoint.

Abstract

On any simply connected Sasaki-Einstein five dimensional manifold one can construct a super Yang-Mills theory which preserves at least two supersymmetries. We study the special case of toric Sasaki-Einstein manifolds known as $Y^{p,q}$ manifolds. We use the localisation technique to compute the full perturbative part of the partition function. The full equivariant result is expressed in terms of certain special function which appears to be a curious generalisation of the triple sine function. As an application of our general result we study the large $N$ behaviour for the case of single hypermultiplet in adjoint representation and we derive the $N^3$-behaviour in this case.