Off-shell Amplitudes in Superstring Theory

TL;DR

This paper develops a practical method for constructing off-shell amplitudes in superstring theory, addressing the challenge of defining such amplitudes with proper factorization, and demonstrates its application in computing effects in heterotic string compactifications.

Contribution

It introduces a systematic procedure using picture changing operators to construct off-shell superstring amplitudes with correct factorization properties, applicable to type II and heterotic strings.

Findings

Constructed off-shell amplitudes satisfying factorization.

Devised a method to handle spurious singularities in superstring perturbation.

Applied the formalism to compute Fayet-Iliopoulos D-terms in heterotic compactifications.

Abstract

Computing the renormalized masses and S-matrix elements in string theory, involving states whose masses are not protected from quantum corrections, requires defining off-shell amplitude with certain factorization properties. While in the bosonic string theory one can in principle construct such an amplitude from string field theory, there is no fully consistent field theory for type II and heterotic string theory. In this paper we give a practical construction of off-shell amplitudes satisfying the desired factorization property using the formalism of picture changing operators. We describe a systematic procedure for dealing with the spurious singularities of the integration measure that we encounter in superstring perturbation theory. This procedure is also useful for computing on-shell amplitudes, as we demonstrate by computing the effect of Fayet-Iliopoulos D-terms in four dimensional heterotic string theory compactifications using this formalism.