AdS_3, Black Holes and Higher Derivative Corrections

TL;DR

This paper argues that in three-dimensional supergravity with (0,4) supersymmetry, higher derivative corrections do not alter the BTZ black hole entropy, due to invariance under field redefinitions and AdS/CFT correspondence.

Contribution

It demonstrates that higher derivative corrections in (0,4) supergravity do not affect black hole entropy, extending previous results through the lens of AdS/CFT.

Findings

Higher derivative corrections can be removed by field redefinitions.

Black hole entropy remains uncorrected by higher derivatives.

AdS/CFT implies non-renormalization of entropy in this context.

Abstract

Using AdS/CFT correspondence and the Euclidean action formalism for black hole entropy Kraus and Larsen have argued that the entropy of a BTZ black hole in three dimensional supergravity with (0,4) supersymmetry does not receive any correction from higher derivative terms in the action. We argue that as a consequence of AdS/CFT correspondence the action of a three dimensional supergravity with (0,4) supersymmetry cannot receive any higher derivative correction except for those which can be removed by field redefinition. The non-renormalization of the entropy then follows as a consequence of this and the invariance of Wald's formula under a field redefinition.