Celestial amplitudes dual to the O(N) nonlinear sigma model

TL;DR

This paper computes celestial amplitudes for the 2D O(N) nonlinear sigma model, revealing their structure as Meijer G-functions and confirming crossing symmetry, thus connecting integrable S-matrices with celestial holography.

Contribution

It provides the first explicit calculation of celestial amplitudes for an integrable 2D quantum field theory, highlighting their mathematical form and symmetry properties.

Findings

Celestial amplitudes are expressed as Meijer G-functions.

Crossing symmetry is explicitly proven for these amplitudes.

Simplifications are discussed for the O(3) symmetry case.

Abstract

We compute celestial amplitudes corresponding to the exact S-matrix of the 2d O(N)-symmetric nonlinear sigma model. Celestial amplitudes for two-dimensional integrable S-matrices simplify to Fourier transforms. Due to the connection between Fourier and Mellin transforms, celestial amplitudes for O(N) model are Mejer G-functions. We also prove crossing symmetry for obtained results and review simplifications for O(3) symmetry case.