Spherical branes

Abstract

We construct new solutions of ten-dimensional supergravity with sixteen super-charges which describe the backreaction of Dp-branes with spherical worldvolume. These solutions are holographically dual to the (p + 1)-dimensional maximally supersymmetric Yang-Mills theory on Sp+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 Dp-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 Sp+1.