Real-time correlators and hidden conformal symmetry in the Kerr/CFT correspondence

Abstract

In this paper, we study the real-time correlators in Kerr/CFT, in the low frequency limit of generic non-extremal Kerr(-Newman) black holes. From the low frequency scattering off Kerr-Newman black holes, we show that for the uncharged scalar scattering, there exists hidden conformal symmetry on the solution space. Similar to Kerr case, this suggests that the Kerr-Newman black hole is dual to a two-dimensional CFT with central charges c L = c R = 12J and temperatures $$ {T_L} = \frac{{\left( {{r_{+} } + {r_{-} }} \right) - {{{{Q^2}}} \left/ {M} \right.}}}{{4\pi a}} $$ , $$ {T_R} = \frac{{{r_{+} } - {r_{-} }}}{{4\pi a}} $$ . Using the Minkowski prescription, we compute the real-time correlators of a charged scalar and find perfect match with CFT prediction. We further discuss the low-frequency scattering of photons and gravitons by a Kerr black hole and find that their retarded Green’s functions are in good agreement with CFT prediction. Our study shows that hidden conformal symmetry in the solution space is essential to set up and check the Kerr/CFT correspondence.