Deconstructing Little Strings with $\mathcal{N}=1$ Gauge Theories on Ellipsoids

TL;DR

This paper refines a formula for perturbative partition functions of $ =1$ gauge theories on ellipsoids, demonstrating its application to Little String Theory via dimensional deconstruction and confirming the theoretical relationship.

Contribution

It extends the perturbative partition function formula to ellipsoids and applies it to connect $ =1$ gauge theories with Little String Theory through deconstruction.

Findings

Partition function formula successfully refined for ellipsoids.

Reproduction of Little String Theory contributions from gauge theory.

Validation of the deconstruction approach linking gauge theories and string theories.

Abstract

A formula was recently proposed for the perturbative partition function of certain $\mathcal N=1$ gauge theories on the round four-sphere, using an analytic-continuation argument in the number of dimensions. These partition functions are not currently accessible via the usual supersymmetric-localisation technique. We provide a natural refinement of this result to the case of the ellipsoid. We then use it to write down the perturbative partition function of an $\mathcal N=1$ toroidal-quiver theory (a double orbifold of $\mathcal N=4$ super Yang-Mills) and show that, in the deconstruction limit, it reproduces the zero-winding contributions to the BPS partition function of (1,1) Little String Theory wrapping an emergent torus. We therefore successfully test both the expressions for the $\mathcal N=1$ partition functions, as well as the relationship between the toroidal-quiver theory and Little String Theory through dimensional deconstruction.