Hidden conformal symmetry of extreme and non-extreme Einstein-Maxwell-dilaton-axion black holes

Abstract

The hidden conformal symmetry of extreme and non-extreme Einstein-Maxwell-Dilaton-Axion (EMDA) black holes is addressed in this paper. For the non-extreme one, employing the wave equation of massless scalars, the conformal symmetry with left temperature $ {T_L} = \frac{M}{{2\pi a}} $ and right temperature $ {T_R} = \frac{{\sqrt {{{M^2} - {a^2}}} }}{{2\pi a}} $ in the near region is found. The conformal symmetry is spontaneously broken due to the periodicity of the azimuthal angle. The microscopic entropy is derived by the Cardy formula and is fully in consistence with the Bekenstein-Hawking area-entropy law. The absorption cross section in the near region is calculated and exactly equals that in a 2D CFT. For the extreme case, by redefining the conformal coordinates, the duality between the solution space and CFT is studied. The microscopic entropy is found to exactly agree with the area-entropy law.