Equivalence of several descriptions for 6d SCFT

TL;DR

This paper demonstrates the equivalence of three different BPS partition functions related to 6d and 5d gauge theories, indicating they share the same UV fixed point, with Type IIB 5-brane webs as a key computational tool.

Contribution

It establishes the equivalence of three seemingly different gauge theory partition functions, revealing a shared UV fixed point and utilizing Type IIB 5-brane webs for the analysis.

Findings

The elliptic genus of 6d $ ext{(1,0)}$ $Sp(1)$ theory equals the Nekrasov functions of 5d $Sp(2)$ and $SU(3)$ theories.

The three partition functions are identical under specific parameter mappings.

Type IIB 5-brane webs are crucial for computing and relating these partition functions.

Abstract

We show that the three different looking BPS partition functions, namely the elliptic genus of the 6d $\mathcal{N}=(1,0)$ $Sp(1)$ gauge theory with $10$ flavors and a tensor multiplet, the Nekrasov partition function of the 5d $\mathcal{N}=1$ $Sp(2)$ gauge theory with $10$ flavors, and the Nekrasov partition function of the 5d $\mathcal{N}=1$ $SU(3)$ gauge theory with $10$ flavors, are all equal to each other under specific maps among gauge theory parameters. This result strongly suggests that the three gauge theories have an identical UV fixed point. Type IIB 5-brane web diagrams play an essential role to compute the $SU(3)$ Nekrasov partition function as well as establishing the maps.