The Sky Remembers everything: Celestial amplitude, Shadow and OPE in quadratic EFT of gravity

TL;DR

This paper explores celestial amplitudes in quadratic gravity, analyzing their structure, phase dressing effects, and operator product expansions within celestial conformal field theory, revealing new insights into higher curvature corrections.

Contribution

It introduces the computation of celestial amplitudes with higher curvature corrections, deriving dispersion relations, and analyzing OPE coefficients in quadratic Einstein gravity.

Findings

Non-vanishing u and s-channel contributions in eikonal limit due to higher curvature terms.

Derived dispersion relation for phase-dressed eikonal amplitude.

Computed OPE coefficients using conformal block expansion and inversion formula.

Abstract

In this paper, we compute the celestial amplitude arising from higher curvature corrections to Einstein gravity, incorporating phase dressing. The inclusion of such corrections leads to effective modifications of the theory's ultraviolet (UV) behaviour. In the eikonal limit, we find that, in contrast to Einstein's gravity, where the $u$ and $s$-channel contributions cancel, these contributions remain non-vanishing in the presence of higher curvature terms. We examine the analytic structure of the resulting amplitude and derive a dispersion relation for the phase-dressed eikonal amplitude in quadratic gravity. Furthermore, we investigate the celestial conformal block expansion of the Mellin-transformed conformal shadow amplitude within the framework of celestial conformal field theory (CCFT). As a consequence, we compute the corresponding operator product expansion (OPE) coefficients using the Burchnall-Chaundy expansion. In addition, we evaluate the OPE via the Euclidean OPE inversion formula across various kinematic channels and comment on its applicability and implications. Finally, we briefly explore the Carrollian amplitude associated with the corresponding quadratic EFT.