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.Physic