General instanton counting and 5d SCFT

TL;DR

This paper develops methods to compute instanton partition functions for 5d SCFTs, revealing symmetry enhancements and addressing UV issues, with implications for understanding higher-dimensional quantum field theories.

Contribution

It introduces integral contour prescriptions for instanton indices using Jeffrey-Kirwan method and explores symmetry enhancements in 5d and 6d SCFTs.

Findings

Instanton indices show E_{N_f+1} symmetry enhancements.

Method for fixing UV incompleteness in 5d SYM theories.

Derived index formulas for gauged quantum mechanics with (0,2) SUSY.

Abstract

Instanton partition functions of 5d N=1 gauge theories are Witten indices for the ADHM gauged quantum mechanics with (0,4) SUSY. We derive the integral contour prescriptions for these indices using the Jeffrey-Kirwan method, for gauge theories with hypermultiplets in various representations. The results can be used to study various 4d/5d/6d QFTs. In this paper, we study 5d SCFTs which are at the UV fixed points of 5d SYM theories. In particular, we focus on the Sp(N) theories with N_f \leq 7 fundamental and 1 antisymmetric hypermultiplets, living on the D4-D8-O8 systems. Their superconformal indices calculated from instantons all show E_{N_f+1} symmetry enhancements. We also discuss some aspects of the 6d SCFTs living on the M5-M9 system. It is crucial to understand the UV incompleteness of the 5d SYM, coming from small instantons in our problem. We explain in our examples how to fix them. As an aside, we derive the index for general gauged quantum mechanics with (0,2) SUSY.