A Modular Invariant Partition Function for the Fivebrane

Abstract

We compute an SL(6,Z) invariant partition function for the chiral two-form of the M theory fivebrane compactified on the six-torus. From a manifestly SL(5,Z) invariant formalism, we prove that the partition function has an additional SL(2,Z) symmetry. The combination of these two symmetries ensures SL(6,Z) invariance. Thus, whether or not a fully covariant Lagrangian is available, the fivebrane on the six-torus has a consistent quantum theory.