M5-branes from gauge theories on the 5-sphere

TL;DR

The paper proposes that 5d maximal SYM on S^5, derived from a Scherk–Schwarz reduction of the 6d (2,0) theory on S^5×S^1, captures the index structure of the 6d theory. Localization yields a perturbative partition function identical to the Chern–Simons partition function on S^3, while a nonperturbative completion reproduces the full 6d index and reveals an index Casimir energy with $N^3$ scaling. In the large-$N$ limit, the index agrees with the gravity index of AdS$_7 imes S^4$, providing microscopic support for the $N^3$ degrees of freedom in M5-branes. The work further extends to generalized 8-SUSY cases with two chemical potentials and discusses broader implications for 6d indices and potential connections to gravity duals and twisted constructions.

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.

Figures (1)

• Figure 1: 2-loop diagrams and the large $N$ double-line diagrams with $N^3$ scalings for $SU(N)$