Exact partition functions of Higgsed 5d $T_N$ theories

TL;DR

This paper develops a systematic method to compute exact partition functions of 5d supersymmetric theories arising from Higgs branches of the $T_N$ theory, including non-toric geometries, and verifies it with examples like the $E_8$ theory.

Contribution

The authors introduce a general prescription for calculating exact partition functions of Higgsed 5d $T_N$ theories, extending to non-toric geometries and confirming with explicit examples.

Findings

Successfully computed partition functions for various Higgs branches of $T_3$.

Explicitly derived the $E_8$ theory partition function and confirmed symmetry enhancement.

Validated the method by matching with known field theory results.

Abstract

We present a general prescription by which we can systematically compute exact partition functions of five-dimensional supersymmetric theories which arise in Higgs branches of the $T_N$ theory. The theories may be realized by webs of 5-branes whose dual geometries are non-toric. We have checked our method by calculating the partition functions of the theories realized in various Higgs branches of the $T_3$ theory. A particularly interesting example is the $E_8$ theory which can be obtained by Higgsing the $T_6$ theory. We explicitly compute the partition function of the $E_8$ theory and find the agreement with the field theory result as well as the enhancement of the global symmetry to $E_8$.