A holographic description of extremal black holes

We show that the extremal Einstein-Maxwell-Dilaton-Axion (EMDA) black hole and the extremal Kaluza-Klein black hole have a hidden conformal symmetry. In this regard, we consider the wave equations of a massless scalar field propagating in EMDA and Kaluza-Klein spacetimes and find in the 'near region', the wave equations in the extremal limit can be written in terms of SL(2, R) Casimir invariants. Moreover, we obtain the microscopic entropy of the extremal EMDA black hole and extremal Kaluza-Klein black hole and find that the correlation function of a near-region scalar field matches the microscopic graybody factor of the dual 2D CFT.