Perturbative partition function for a squashed S^5

TL;DR

This paper calculates the perturbative partition function of 6d N=(1,0) theories on a squashed five-sphere by compactifying a circle with twisted boundary conditions, resulting in a simple expression involving the triple sine function.

Contribution

It introduces a method to derive the perturbative partition function on a squashed S^5 using compactification and small radius limit, expressed with the triple sine function.

Findings

Derived the perturbative partition function for 6d N=(1,0) theories on squashed S^5.

Expressed the 1-loop partition function in a simple form using the triple sine function.

Focused on the perturbative sector without instantons.

Abstract

We compute the index of 6d N=(1,0) theories on S^5 x R containing vector and hypermultiplets. We only consider the perturbative sector without instantons. By compactifying R to S^1 with a twisted boundary condition and taking the small radius limit, we derive the perturbative partition function on a squashed S^5. The 1-loop partition function is represented in a simple form with the triple sine function.