Black hole entropy in M theory

Extremal black holes in M-theory compactification on M × S1 are microscopically represented by fivebranes wrapping P × S1, where M is a Calabi-Yau threefold and P is a four-cycle in M. Additional spacetime charges arise from momentum around the S1 and expectation values for the self-dual three-form field strength in the fivebrane. The microscopic entropy of the fivebrane as a function of all the charges is determined from a two-dimensional (0,4) sigma model whose target space includes the fivebrane moduli space. This entropy is compared to the macroscopic formula. Precise agreement is found for both the tree-level and one-loop expressions.