Wrapped M2/M5 duality

A microscopic accounting of the entropy of a generic 5D supersymmetricrotating black hole, arising from wrapped M2-branes in Calabi-Yau compactifiedM-theory, is an outstanding unsolved problem. In this paper we consider anexpansion around the zero-entropy, zero-temperature, maximally rotating groundstate for which the angular momentum J_L and graviphoton charge Q are relatedby J_L^2=Q^3. At J_L=0 the near horizon geometry is AdS_2 x S^3. As J_L^2 goesto Q^3 it becomes a singular quotient of AdS_3 x S^2: more precisely, aquotient of the near horizon geometry of an M5 wrapped on a 4-cycle whoseself-intersection is the 2-cycle associated to the wrapped-M2 black hole. Thesingularity of the AdS_3 quotient is identified as the usual one associated tothe zero-temperature limit, suggesting that the (0,4) wrapped-M5 CFT is dualnear maximality to the wrapped-M2 black hole. As evidence for this, themicroscopic (0,4) CFT entropy and the macroscopic rotating black hole entropyare found to agree to leading order away from maximality.Comment: 10 pages, no figure