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.
Highlights
Brane solutions in supergravity have offered multiple important insights into the structure of string theory, supergravity, and holography
In this paper we constructed explicit supergravity solutions which preserve sixteen real supercharges and describe the backreaction of spherical Dp-branes with 1 ≤ p ≤ 6. We argued that these backgrounds are holographically dual to the planar limit of the maximally supersymmetric Yang-Mills theory on Sp+1
An immediate consistency check of this claim is provided by the fact that the global symmetries and supersymmetry of the gauge theory and the supergravity solutions are the same
Summary
Brane solutions in supergravity have offered multiple important insights into the structure of string theory, supergravity, and holography. These scalar fields are the supergravity manifestation of the running gauge coupling of SYM theory and the couplings in the Lagrangian on Sp+1 that need to be turned on to preserve supersymmetry Working with this p + 2-dimensional gauged supergravity we are able to construct explicitly the supersymmetric spherical domain wall solutions of interest and use standard uplift formulae from the literature to convert them to solutions of type II supergravity. In the UV region of the spherical brane solutions the background is the same as the near-horizon limit of the usual flat Dpbrane backgrounds [1], albeit with Euclidean worldvolume This behavior is in line with the dual gauge theory where at high energies the radius of the sphere should not affect the dynamics and one expects to recover the physics of SYM theory in flat space. In the three appendices we present our conventions, review the known flat Euclidean D-brane solutions of type II supergravity, and summarize the various lowerdimensional gauged supergravity theories used to construct the spherical brane solutions
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