Observations on Open and Closed String Scattering Amplitudes at High Energies

TL;DR

This work analyzes high-energy massless string scattering in flat space, showing that under formal T-duality open-string amplitudes are governed by the exponential of minimal-area surfaces bounded by cusped lightlike loops, while closed-string amplitudes arise from gluing two such surfaces, reflecting a flat-space KLT structure. It develops Douglas' method as the boundary-variation (T-dual) approach and provides explicit lower-point amplitudes, including multi-cross-ratio Douglas functionals for 4–6 points. The authors then connect these flat-space results to AdS/CFT by proposing a similar gluing picture for graviton amplitudes (and potentially $\mathcal{N}=8$ supergravity) and by relating correlator/amplitude duality to a KLT-like double-copy. Overall, the paper highlights a geometric, minimal-surface perspective on high-energy string amplitudes and their double-copy structure, with extensions and conjectures in AdS/CFT and quantum gravity contexts.

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.

Figures (5)

• Figure 1: The vertex insertion points are mapped to the lightlike segments, and the intervals between them are mapped to the cusps.
• Figure 2: Two disks glued along the cusped closed lightlike boundary to form a sphere. In flat space the actual sphere is flattened.
• Figure 3: Two copies of Alday-Maldacena's minimal surfaces glued to yield graviton scattering amplitudes at high energies in AdS via the KLT relation.
• Figure 4: The minimal surfaces for correlators. The right figure represents the degenerate surface after the null separation limit of the surface on the left is taken. The zigzag line forms a closed lightlike loop on the boundary.
• Figure A: $N$-point Mandelstam variables.