Multi-loop open string amplitudes and their field theory limit

TL;DR

This paper explores the connection between multi-loop string amplitudes and field theory Feynman diagrams, providing a detailed map that clarifies how string theory reduces to field theory in the low-energy limit, especially for open strings on D-branes.

Contribution

It introduces an explicit mapping between string moduli and Feynman parameters, clarifies ambiguities in supermoduli integration, and demonstrates the approach with two-loop examples in bosonic and RNS string theories.

Findings

Established a correspondence between string moduli and Feynman parameters.

Clarified the integration prescription over supermoduli for consistency.

Presented two-loop examples illustrating the string-field theory connection.

Abstract

We study the field theory limit of multi-loop (super)string amplitudes, with the aim of clarifying their relationship to Feynman diagrams describing the dynamics of the massless states. We propose an explicit map between string moduli around degeneration points and Schwinger proper-times characterizing individual Feynman diagram topologies. This makes it possible to identify the contribution of each light string state within the full string amplitude and to extract the field theory Feynman rules selected by (covariantly quantized) string theory. The connection between string and field theory amplitudes also provides a concrete tool to clarify ambiguities related to total derivatives over moduli space: in the superstring case, consistency with the field theory results selects a specific prescription for integrating over supermoduli. In this paper, as an example, we focus on open strings supported by parallel D-branes, and we present two-loop examples drawn from bosonic and RNS string theories, highlighting the common features between the two setups.