The Ramond-Ramond self-dual Five-form's Partition Function on the Ten Torus

TL;DR

This paper constructs an SL(10,Z) invariant partition function for the self-dual five-form in Type IIB string theory on a ten-torus, extending methods from M-theory and exploring automorphic forms for higher dimensions.

Contribution

It provides the first explicit SL(10,Z) invariant partition function for the chiral four-form in Type IIB string theory, generalizing to self-dual fields in higher dimensions.

Findings

Derived a modular invariant partition function for the chiral four-form.

Extended the calculation to self-dual fields in dimensions 2p=2+4k.

Connected the results to B-cycle period computations by Witten.

Abstract

In view of the recent interest in formulating a quantum theory of Ramond-Ramond p-forms, we exhibit an SL(10,Z) invariant partition function for the chiral four-form of Type IIB string theory on the ten-torus. We follow the strategy used to derive a modular invariant partition function for the chiral two-form of the M-theory fivebrane. We also generalize the calculation to self-dual quantum fields in spacetime dimension 2p=2+4k, and display the SL(2p,Z) automorphic forms for odd p>1. We relate our explicit calculation to a computation of the B-cycle periods, which are discussed in the work of Witten.