Scattering amplitudes for cylindrical gravitational waves

TL;DR

This paper computes the 2-particle tree-level S-matrix for cylindrical gravitational waves, revealing symmetry properties linked to Geroch symmetry through a dimensional reduction to a nonlinear sigma model.

Contribution

It provides the first calculation of the S-matrix for cylindrical gravitational waves using a reduced 2D model, highlighting symmetry features.

Findings

Derived the 2-particle tree-level S-matrix for cylindrical gravitational waves.

Identified an SO(2) symmetry as a subset of Geroch symmetry in the amplitudes.

Connected the reduced model to a nonlinear sigma model framework.

Abstract

Cylindrical gravitational waves are interesting because they enjoy an infinite dimensional symmetry called Geroch symmetry. In this paper, we compute the 2-particle tree-level S-matrix for cylindrical gravitational waves. The model we use is a dimensional reduction of general relativity to two spacetime dimensions. The reduced theory is a nonlinear sigma model. We discuss an SO(2) symmetry of the amplitudes which is a special case of Geroch symmetry.