Analyticity of Off-shell Green's Functions in Superstring Field Theory

TL;DR

This paper investigates the analyticity properties of off-shell Green's functions in superstring field theory, extending known results from local QFTs and analyzing the domain of analyticity for multi-point functions.

Contribution

It extends the domain of analyticity for off-shell Green's functions in superstring field theory using complex Lorentz transformations and Bochner's theorem, recovering the full primitive domain for 2-4 points.

Findings

Full primitive domain recovered for 2-, 3-, and 4-point functions.

Partial domain recovery for 5-point functions.

Analyticity extension techniques applicable to higher-point functions.

Abstract

We consider the off-shell momentum space Green's functions in closed superstring field theory. Recently in arXiv:1810.07197, the off-shell Green's functions -- after explicitly removing contributions of massless states -- have been shown to be analytic on a domain (to be called the LES domain) in complex external momenta variables. Analyticity of off-shell Green's functions in local QFTs without massless states in the primitive domain is a well-known result. Using complex Lorentz transformations and Bochner's theorem allow to extend the LES domain to a larger subset of the primitive domain. For the 2-, 3- and 4-point functions, the full primitive domain is recovered. For the 5-point function, we are not able to obtain the full primitive domain analytically, only a large part of it is recovered. While this problem arises also for higher-point functions, it is expected to be only a technical issue.