Spherical Branes and the BMN Matrix Quantum Mechanics

TL;DR

This paper connects supersymmetric Yang-Mills theory on spheres to the BMN matrix model via analytic continuation, providing explicit results for free energy and Wilson loops at large N using localisation and holography.

Contribution

It introduces a novel analytic continuation from higher-dimensional SYM to the BMN matrix quantum mechanics and constructs spherical D-brane solutions for arbitrary dimensions.

Findings

Explicit large N free energy on $S^d$

Expectation values of supersymmetric Wilson loops

Holographic duals via spherical D-brane solutions

Abstract

We study the maximally supersymmetric Yang-Mills theory on $S^d$ using supersymmetric localisation and holography. We argue that the analytic continuation in dimension to $d=1$ yields a Euclidean version of the BMN matrix quantum mechanics. This system can be analysed at large $N$ using supersymmetric localisation and leads to explicit results for the free energy on $S^d$ and the expectation value of supersymmetric Wilson loops. We show how these results can be reproduced at strong gauge coupling using holography by employing spherical D-brane solutions. We construct these solutions for any value of $d$ using an effective supergravity description and pay particular attention to the subtleties arising in the $d\to1$ limit. Our results have implications for the BMN matrix quantum mechanics and the physics of circular D0-branes.