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.