Hidden conformal symmetry of the Kerr black hole

Extreme and very-near-extreme spin J Kerr black holes have been conjectured to be holographically dual to two-dimensional (2D) conformal field theories (CFTs) with left and right central charges c(L) = c(R) = 12J. In this paper it is observed that the 2D conformal symmetry of the scalar wave equation at low frequencies persists for generic nonextreme values of the mass M not equal root J. Interestingly, this conformal symmetry is not derived from a conformal symmetry of the spacetime geometry except in the extreme limit. The 2 pi periodic identification of the azimuthal angle phi is shown to correspond to a spontaneous breaking of the conformal symmetry by left and right temperatures T-L = M-2/2 pi J and T-R = root M-4 - J(2)/2 pi J. The well-known low-frequency scalar-Kerr scattering amplitudes coincide with correlators of a 2D CFT at these temperatures. Moreover, the CFT microstate degeneracy inferred from the Cardy formula agrees exactly with the Bekenstein-Hawking area law for all M and J. These observations provide evidence for the conjecture that the Kerr black hole is dual to a c(L) = c(R) = 12J 2D CFT at temperatures (T-L, T-R) for every value of M and J.