Spherical Branes

TL;DR

This paper constructs new supergravity solutions representing spherical D$p$-branes, providing a holographic dual to maximally supersymmetric Yang-Mills theory on spheres, and confirms the solutions match localization results for free energy.

Contribution

It introduces novel supergravity backgrounds with spherical branes that serve as holographic duals to SYM theories on spheres, extending previous flat-brane models.

Findings

Supergravity solutions describe spherical D$p$-branes with smooth geometry.

On-shell action matches supersymmetric localization results.

Solutions provide IR cutoff via sphere's finite size.

Abstract

We construct new solutions of ten-dimensional supergravity with sixteen supercharges which describe the backreaction of D$p$-branes with spherical worldvolume. These solutions are holographically dual to the $(p+1)$-dimensional maximally supersymmetric Yang-Mills theory on $S^{p+1}$. The finite size of the sphere provides an IR cut-off for the gauge theory which is manifested in the supergravity solution as a smooth cap-off of the geometry. In the UV the size of the sphere plays no role and the backgrounds asymptote to the well-known supergravity solutions that describe the near-horizon limit of flat D$p$-branes. We compute the on-shell action of our spherical brane solutions and show that it is in agreement with recent supersymmetric localization results for the free energy of maximal SYM theory on $S^{p+1}$.