High energy scattering of non-critical strings

TL;DR

This paper analyzes high energy scattering amplitudes of non-critical strings, revealing a saddle point dominated by electrostatic equilibrium configurations that influence the string's behavior, with explicit solutions for 3- and 4-point functions.

Contribution

It introduces a novel electrostatic analogy for high energy non-critical string scattering and provides explicit solutions for key scattering amplitudes.

Findings

High energy limit dominated by electrostatic saddle point.

Explicit solutions for 3- and 4-point functions using hyperelliptic integrals.

High energy behavior remains string-like with exponential energy dependence.

Abstract

We summarize recent work, in which we consider scattering amplitudes of non-critical strings in the limit where the energy of all external states is large compared to the string tension. We show that the high energy limit is dominated by a saddle point that can be mapped onto an electrostatic equilibrium configuration of an assembly of charges associated with the external states, together with a density of charges arising from the Liouville field. The Liouville charges accumulate on line segments, which produce quadratic branch cuts on the worldsheet. The electrostatics problem is solved for string tree level in terms of hyperelliptic integrals and is given explicitly for the 3- and 4-point functions. For generic values of the central charge, the high energy limit behaves in a string-like fashion, with exponential energy dependence.