M5-branes from gauge theories on the 5-sphere

TL;DR

This paper uses supersymmetric gauge theory partition functions on the 5-sphere to study the (2,0) superconformal theory, revealing connections to Chern-Simons theory, BPS states, and supergravity predictions.

Contribution

It demonstrates how 5d gauge theories encode 6d superconformal data and matches supergravity indices, providing new insights into M5-brane dynamics.

Findings

Casimir energy scales as N^3 at large N

Partition functions relate to Chern-Simons theory on S^3

Large N index matches supergravity predictions

Abstract

We use the 5-sphere partition functions of supersymmetric Yang-Mills theories to explore the (2,0) superconformal theory on S^5 x S^1. The 5d theories can be regarded as Scherk-Schwarz reductions of the 6d theory along the circle. In a special limit, the perturbative partition function takes the form of the Chern-Simons partition function on S^3. With a simple non-perturbative completion, it becomes a 6d index which captures the degeneracy of a sector of BPS states as well as the index version of the vacuum Casimir energy. The Casimir energy exhibits the N^3 scaling at large N. The large N index for U(N) gauge group also completely agrees with the supergravity index on AdS_7 x S^4.