Some global issues in string perturbation theory

Abstract

Calculations of the type II string vacuum amplitude using the picture changing prescription have been shown to lead, in general, to a positive cosmological constant. We show that there is a global obstruction to the choices of gauge slice for super-Teichmüller space that lead to such measures. We discuss the general restrictions on gauge slices appropriate for use in explicit fermionic string calculations. We also discuss the relation of the functional determinant and conformal field theory versions of the path integral measure, and show that, at arbitrary genus and in arbitrary backgrounds preserving tree level N=1 supersymmetry, the measure is an exact differential. We evaluate the boundary integrals of this total derivative at genus two in two ways for target space R¹⁰ to show that the integrals are zero. Finally, we use the factorization hypothesis to show that in appropriate compactified spacetimes the boundary integrals continue to vanish.