A Dynamical Brane in the Gravitational Dual of ${\cal N}=2$ $Sp(N)$ Superconformal Field Theory

TL;DR

This paper constructs a perturbative AdS black hole solution in a higher derivative gravity model dual to ${ m N}=2$ $Sp(N)$ SCFT, revealing a dynamical brane outside the horizon consistent with AdS/CFT.

Contribution

It introduces a perturbative black hole solution in a higher derivative gravity dual to ${ m N}=2$ $Sp(N)$ SCFT and demonstrates the dynamical brane's position relative to the horizon.

Findings

Dynamical brane always outside the horizon.

Surface counterterms ensure well-defined variational principle.

Parameters are fixed by AdS/CFT correspondence constraints.

Abstract

The particular model of d5 higher derivative gravity which is dual to ${\cal N}=2$ $Sp(N)$ SCFT is considered. A (perturbative) AdS black hole in such theory is constructed in the next-to-leading order of the AdS/CFT correspondence. The surface counterterms are fixed by the conditions required for a well-defined variational procedure and the finiteness of AdS space (when the brane goes to infinity). A dynamical brane is realized at the boundary of an AdS black hole with a radius that is larger than the horizon radius. The AdS/CFT correspondence dictates the parameters of the gravitational dual in such a way that the dynamical brane (the observable universe) always occurs outside the horizon.