Black hole entropy in M-Theory

Extremal black holes in M-theory compactification on $M\times S^1$ aremicroscopically represented by fivebranes wrapping $P\times S^1$, where $M$ isa Calabi-Yau threefold and $P$ is a four-cycle in $M$. Additional spacetimecharges arise from momentum around the $S^1$ and expectation values for theself-dual three-form field strength in the fivebrane. The microscopic entropyof the fivebrane as a function of all the charges is determined from atwo-dimensional $(0,4)$ sigma model whose target space includes the fivebranemoduli space. This entropy is compared to the macroscopic formula. Preciseagreement is found for both the tree-level and one-loop expressions.Comment: 17 pages, harvma