Analyticity Domain for Off-shell Five-point Superstring Loop Amplitudes

TL;DR

This paper extends the analytic domain of off-shell five-point superstring loop amplitudes by identifying convex combinations that cover previously unresolved primitive tubes, using algorithms and numerical methods.

Contribution

It introduces a new algorithm to analytically cover remaining primitive tubes in superstring amplitudes and suggests potential for complete coverage with further improvements.

Findings

Successfully identified 129 convex combination types for primitive tubes.

Numerical analysis found points not covered by current convex combinations.

Proposed methods indicate possible full coverage of all primitive tubes.

Abstract

In an earlier work arXiv:2009.0337, we showed that for arbitrary Feynman loop diagrams (with no massless internal propagators) in closed superstring field theory, a known domain can be analytically extended by simply adjoining convex combinations of points drawn from it. Such extension yielded 350 of the well-known 370 primitive tubes for 5-point functions. In this paper, we consider the remaining 20 primitive tubes. We show that different types of convex combinations cover different sections of these tubes. We use a specific algorithm to analytically obtain 129 types of convex combinations along with their region of validity. Then, we use numerical techniques to locate points from those tubes that are not covered by them. This does not rule out the possibility of the leftover points being represented as desirable convex combinations. Indeed we give ways to improve our algorithm indicating that the leftover points can be covered.