Wrapped \(M2/M5\) Duality

Abstract

A microscopic accounting of the entropy of a generic 5D supersymmetric rotating black hole, arising from wrapped (M2)-branes in Calabi-Yau compactified (M)-theory, is an outstanding unsolved problem. In this paper we consider an expansion around the zero-entropy, zero-temperature, maximally rotating ground state for which the angular momentum (J_L) and graviphoton charge (Q) are related by ({J_L}^2 = Q^3). At (J_L = 0) the near horizon geometry is (AdS_2 × S^3). As ({J_L}^2 → Q^3) it becomes a singular quotient of (AdS_3 × S^2): more precisely, a quotient of the near horizon geometry of an (M5) wrapped on a 4-cycle whose self-intersection is the 2-cycle associated to the wrapped-(M2) black hole. The singularity of the (AdS_3) quotient is identified as the usual one associated to the zero-temperature limit, suggesting that the (0,4) wrapped-(M5) CFT is dual near maximality to the wrapped-(M2) black hole. As evidence for this, the microscopic (0,4) CFT entropy and the macroscopic rotating black hole entropy are found to agree to leading order away from maximality.