Wrapped M2/M5 Duality

TL;DR

This paper explores the duality between wrapped M2 and M5 branes in M-theory, providing a microscopic accounting of 5D black hole entropy near maximal rotation and establishing a duality with a (0,4) CFT.

Contribution

It introduces a new duality framework relating wrapped M2 and M5 branes, and matches microscopic and macroscopic entropies near maximal rotation.

Findings

Microscopic (0,4) CFT entropy matches black hole entropy at leading order.

Near maximal rotation, the geometry becomes a quotient of AdS_3 x S^2.

The singularity corresponds to the zero-temperature limit of the dual CFT.

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 x S^3. As J_L^2 goes to Q^3 it becomes a singular quotient of AdS_3 x 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.