A Modular Invariant Partition Function for the Fivebrane

TL;DR

This paper constructs an SL(6,Z) invariant partition function for the M theory fivebrane's chiral two-form on a six-torus, demonstrating its quantum consistency through symmetry analysis.

Contribution

It introduces a novel SL(6,Z) invariant partition function and proves an additional SL(2,Z) symmetry, ensuring the fivebrane's quantum consistency without requiring a fully covariant Lagrangian.

Findings

Partition function is SL(6,Z) invariant.

Proves an SL(2,Z) symmetry of the partition function.

Establishes quantum consistency of the fivebrane on the six-torus.

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.