Spherical branes and the BMN matrix quantum mechanics

Abstract

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 → 1 limit. Our results have implications for the BMN matrix quantum mechanics and the physics of circular D0-branes.

Keywords

• AdS-CFT Correspondence
• Gauge-Gravity Correspondence
• D-Branes
• Supersymmetric Gauge Theory