AdS₃, Black Holes and Higher Derivative Corrections

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.