Scalar field theory limits of bosonic string amplitudes

TL;DR

This paper details the methods for deriving scalar field theory limits from bosonic string amplitudes up to two loops, focusing on the correct combinatorial and color factors through moduli space analysis.

Contribution

It introduces a comprehensive technique for computing scalar amplitudes from string theory, applicable to various interactions and diagram types, with precise moduli space integration.

Findings

Derived scalar field theories in renormalizable dimensions

Established methods for planar and non-planar diagram calculations

Provided detailed moduli space integration techniques

Abstract

We describe in detail the techniques needed to compute scattering amplitudes for colored scalars from the infinite tension limit of bosonic string theory, up to two loops. These techniques apply both to cubic and quartic interactions, and to planar as well as non-planar diagrams. The resulting field theories are naturally defined in the space-time dimension in which they are renormalizable. With a careful analysis of string moduli space in the Schottky representation we determine the region of integration for the moduli, which plays a crucial role in the derivation of the correct combinatorial and color factors for all diagrams.