Perturbative diagrams in string field theory

TL;DR

This paper introduces a general algorithm for deriving closed-form expressions of perturbative diagrams in cubic string field theory, enabling finite matrix approximations for complex calculations at any loop order.

Contribution

It presents a novel algorithm that expresses perturbative diagrams as integrals over infinite matrices, which can be approximated by finite matrices through level truncation.

Findings

Derived closed-form expressions for diagrams at any loop order

Demonstrated finite matrix approximation via level truncation

Worked out examples of simple tree and loop diagrams

Abstract

A general algorithm is presented which gives a closed-form expression for an arbitrary perturbative diagram of cubic string field theory at any loop order. For any diagram, the resulting expression is given by an integral of a function of several infinite matrices, each built from a finite number of blocks containing the Neumann coefficients of Witten's 3-string vertex. The closed-form expression for any diagram can be approximated by level truncation on oscillator level, giving a computation involving finite size matrices. Some simple tree and loop diagrams are worked out as examples of this approach.