# Scattering amplitudes of regularized bosonic strings

## TL;DR

This paper calculates scattering amplitudes of a regularized bosonic string using mean-field approximation, showing Regge behavior and stability of the effective action minimum in certain dimensions.

## Contribution

It introduces a mean-field approach to compute string scattering amplitudes and demonstrates Regge behavior in the Lilliputian scaling limit.

## Key findings

- Regge behavior of amplitudes recovered in the limit
- Stability of the effective action minimum for dimensions less than 26
- Use of mean-field approximation disregarding fluctuations

## Abstract

We compute scattering amplitudes of the regularized bosonic Nambu-Goto string in the mean-field approximation, disregarding fluctuations of the Lagrange multiplier and an independent metric about their mean values. We use the previously introduced Lilliputian scaling limit to recover the Regge behavior of the amplitudes with the usual linear Regge trajectory in space-time dimensions d>2. We demonstrate a stability of this minimum of the effective action under fluctuations for d<26.