Integrable Field Theories and Their CCFT Duals

TL;DR

This paper explicitly computes Mellin transforms of 2D integrable S-matrices, providing the first non-perturbative celestial CFT realizations, and explores their analytic properties and gravitational couplings.

Contribution

It introduces explicit non-perturbative Mellin transforms of 2D integrable S-matrices as celestial CFT correlators, analyzing their properties and gravitational effects.

Findings

Correlators are real distributions in conformal weights.

Asymptotics are governed by mass spectrum and couplings.

Gravity coupling smooths out singularities in correlators.

Abstract

We compute the Mellin transforms of various two-dimensional integrable $S$-matrices, providing the first explicit, non-perturbative realizations of celestial CFT. In two dimensions, the Mellin transform is simply the Fourier transform in rapidity space, and the "celestial correlator" has no position dependence. The simplified setting allows us to study the analytic properties of CCFT correlators exactly as a function of the conformal dimensions. We find that the correlators exist as real distributions of the conformal weights, with asymptotics controlled by the mass spectrum and three-point couplings of the model. Coupling these models to a flat space limit of JT gravity preserves integrability and dresses the amplitudes by a rapidly varying gravitational phase. We find that the coupling to gravity smooths out certain singular aspects of the Mellin-transformed correlators.