# Varying dilaton as a tracer of classical string interactions

## TL;DR

This paper investigates tree-level string amplitudes in a linear dilaton background to serve as a gauge-invariant tracer of string interactions, revealing how dilaton variation influences interaction timescales and non-locality.

## Contribution

It introduces a method to analyze string interactions using a linear dilaton background, accounting for zero mode effects and providing finite, physically meaningful results.

## Key findings

- Reproduces expected interaction timescales in string scattering
- Highlights interplay between dilaton effects and the $i\epsilon$ prescription
- Suggests a way to trace non-locality in string interactions

## Abstract

We analyze tree-level string amplitudes in a linear dilaton background, motivated by its use as a gauge-invariant tracer of string interactions in scattering experiments and its genericity among simple perturbative string theory limits. A simple case is given by a lightlike dependence for the dilaton. The zero mode of the embedding coordinate in the direction of dilaton variation requires special care. Employing Gaussian wave packets and a well-defined modification of the dilaton profile far from the dominant interaction region, we obtain finite results which explicitly reproduce the interaction timescales expected from joining and splitting interactions involving oscillating strings in simple string scattering processes. There is an interesting interplay between the effects of the linear dilaton and the $i\epsilon$ prescription. In more general circumstances this provides a method for tracing the degree of non-locality in string interactions, and it gives a basis for further studies of perturbative supercritical string theory at higher loop order.