Global structure of the superstring partition function and resolution of the supermoduli measure ambiguity

Abstract

We investigate the global structure of the fermionic string partition function on the supermoduli space M g sup. In particular we show how the recently discovered moduli total-derivative ambiguity is due to a non-trivial cocycle on M g sup, present if an atlas of coordinates of M g sup can be found, whose transition functions contain even, nilpotent components. We find a correction to the usual Berezin measure on M g sup, given by the so-called Rothstein volume form, that eliminates the above boundary ambiguities of the supermoduli measure at any genus. We discuss also the so-called theorem of holomorphic factorization in this particular case and its relation to the physical requirement of modular invariance.