Perturbative partition function for a squashed S^5

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.

24 pages, 1 figure; v2: references added, errors corrected, explanations added; v3: explanations improved, errors corrected, an overall factor added to the final result