Integrable Field Theories and Their CCFT Duals

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.

26 pages, 2 figures

References in corpus (9)

• The BMS/GCA correspondence
• Gluon Amplitudes as 2d Conformal Correlators
• On Effective Field Theories with Celestial Duals
• Celestial holography on Kerr-Schild backgrounds
• Celestial Liouville Theory for Yang-Mills Amplitudes
• Loop-level gluon OPEs in celestial holography
• Four-point correlators of light-ray operators in CCFT
• Notes on Resonances and Unitarity from Celestial Amplitudes
• Celestial amplitude for 2d theory

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• Flat limit of massless scalar scattering in ${\mathrm{AdS}}_2$