On Factorizing Correlation Functions in String Theory Using Loop Variables

TL;DR

This paper introduces a method to factorize string theory correlation functions using loop variables, enabling the construction of interaction vertices that correctly reproduce S-matrix elements, even with off-shell particles.

Contribution

The paper presents a novel approach to factorize string correlation functions with loop variables, ensuring accurate S-matrix reproduction for off-shell particles.

Findings

Successful factorization of string correlation functions using loop variables

Construction of interaction vertices that reproduce S-matrix elements

Examples demonstrating off-shell particle incorporation

Abstract

Factorization of string amplitudes is one way of constructing string interaction vertices. We show that correlation functions in string theory can be conveniently factorized using loop variables representing delta functionals. We illustrate this construction with some examples where one particle is off-shell. These vertices are ``correct'' in the sense that they are guaranteed, by construction, to reproduce S-matrix elements when combined with propagators in a well defined way.