Instantons on the 5-sphere and M5-branes

TL;DR

This paper computes supersymmetric gauge theory partition functions on S^5, revealing non-perturbative instanton effects and matching results with gravity duals for 6d (2,0) theories, advancing understanding of M5-branes.

Contribution

It introduces a novel calculation of instanton contributions to S^5 partition functions and connects these to 6d (2,0) theory indices, including gravity dual comparisons.

Findings

Instanton loops localize to three fixed points on CP^2.

Partition functions match gravity dual indices in large N limit.

Abelian case results agree with free 6d tensor supermultiplet index.

Abstract

We calculate the partition functions of supersymmetric gauge theories on S^5, which acquire non-perturbative contributions from instanton loops wrapping its Hopf fiber. The instantons on the CP^2 base equivariantly localize to 3 fixed points of SU(3) Cartans. Using our results, we study the index of the 6d (2,0) theory. We first study the partition functions of maximal SYM with AD(E) gauge groups, which agree with the gravity dual indices on AdS_7 in the large N limits. We also show that the most general partition function of the Abelian theory agrees with the index for a free 6d tensor supermultiplet. We explain possible ambiguities in our 5d approach, role of maximal SUSY, and the Wilson loops on S^5 dual to M2-brane Wilson surfaces in AdS_7.