Observations on Open and Closed String Scattering Amplitudes at High Energies

TL;DR

This paper investigates high-energy open and closed string scattering amplitudes in flat space, revealing their geometric interpretation via minimal surfaces and exploring their relation to the KLT relation and dualities in string theory.

Contribution

It demonstrates that open string amplitudes at high energies are related to minimal surfaces with cusped boundaries and shows how closed string amplitudes can be constructed from these, extending the KLT relation.

Findings

Open string amplitudes are exponential of minimal surface areas.

Closed string amplitudes are formed by gluing two minimal surfaces.

Connection between high-energy string amplitudes and geometric minimal surfaces.

Abstract

We study massless open and closed string scattering amplitudes in flat space at high energies. Similarly to the case of AdS space, we demonstrate that, under the T-duality map, the open string amplitudes are given by the exponential of minus minimal surface areas whose boundaries are cusped closed loops formed by lightlike momentum vectors. We show further that the closed string amplitudes are obtained by gluing two copies of minimal surfaces along their cusped lightlike boundaries. This can be thought of as a manifestation of the Kawai-Lewellen-Tye (KLT) relation at high energies. We also discuss the KLT relation in AdS/CFT and its possible connection to amplitudes in N=8 supergravity as well as the correlator/amplitude duality.