On the Zero-Slope Limit of the Compactified Closed Bosonic String

TL;DR

This paper investigates the zero-slope and small-radius limits of the four-point scattering amplitude in compactified closed bosonic string theory, revealing connections to scalar, vector, and tensor exchanges, including linearized gravity.

Contribution

It explicitly demonstrates how these limits produce effective interactions involving scalars, vectors, and gravitons, linking string amplitudes to field theory results.

Findings

Limits reproduce scalar, vector, and tensor exchanges

Results align with linearized quantum gravity

Clarifies the low-energy behavior of compactified strings

Abstract

In the framework of the compactified closed bosonic string theory with the extra spatial coordinates being circular with radius $R$, we perform both the zero-slope limit and the $R \rightarrow 0$ limit of the tree scattering amplitude of four massless scalar particles. We explicitly show that this double limit leads to amplitudes involving scalars which interact through the exchange of a scalar, spin 1 and spin 2 particle. In particular, this latter case reproduces the same result obtained in linearized quantum gravity.