Notes on 5d Partition Functions -- II

TL;DR

This paper investigates the large N behavior of partition functions in 5d supersymmetric gauge theories, revealing different scaling laws depending on matter content and connecting to 3d theories with M-theory duals.

Contribution

It identifies conditions under which 5d partition functions scale as N^2 or N^{3/2} and links these results to 3d theories from 5d SCFT compactifications.

Findings

Partition functions scale as N^2 or N^{3/2} depending on matter content.

The N^{3/2} scaling resembles 3d theories with M-theory duals.

Method to extract scaling behavior from 3d theories associated with 5d SCFTs.

Abstract

We study the large $N$ limit of partition functions for 5d supersymmetric gauge theories with fundamental matter. Depending on the matter content, we find that the scaling behaviour at the leading order can be either $N^2$ or $N^{\frac{3}{2}}$. The latter scaling reminds one of the 3d theories with M-theory duals and we discuss how to extract this behaviour from the recently proposed 3d theories associated with the compactification of 5d SCFTs on 2d surfaces.