Microscopic Realization of the Kerr/CFT Correspondence

Abstract

Supersymmetric M/string compactifications to five dimensions contain BPS black string solutions with magnetic graviphoton charge (P) and near-horizon geometries which are quotients of (AdS 3 \times S^2). The holographic duals are typically known 2D CFTs with central charges (c L = c R = 6P^3) for large (P). These same 5D compactifications also contain non-BPS but extreme Kerr-Newman black hole solutions with (SU(2)) Lspin (J L) and electric graviphoton charge (Q) obeying (Q^3 \le J L^2). It is shown that in the maximally charged limit (Q^3 \rightarrow J L^2), the near-horizon geometry coincides precisely with the right-moving temperature (T R = 0) limit of the black string with magnetic charge (P = J L^\frac{1}{3}). The known dual of the latter is identified as the (cL = c R =6J L) CFT predicted by the Kerr/CFT correspondence. Moreover, at linear order away from maximality, one finds a (T R \not= 0) quotient of the AdS 3 factor of the black string solution and the associated thermal CFT entropy reproduces the linearly sub-maximal Kerr-Newman entropy. Beyond linear order, for general (Q^3 < J L^2), one has a finite-temperature quotient of a warped deformation of the magnetic string geometry. The corresponding dual deformation of the magnetic string CFT potentially supplies, for the general case, the (c L = c R =6J L) CFT predicted by Kerr/CFT.