Carrollian propagator and amplitude in Rindler spacetime

TL;DR

This paper explores the structure of Carrollian field theory on Rindler horizons, establishing propagators and amplitudes that connect to bulk scalar fields and revealing novel relationships between four-point and three-point amplitudes.

Contribution

It constructs boundary-to-boundary and bulk-to-boundary propagators for Carrollian fields in Rindler spacetime and analyzes their amplitudes, linking them to Feynman integrals and lower-point functions.

Findings

Four-point Carrollian amplitude resembles a one-loop Feynman integral.

Zero energy insertion amplitude relates to three-point amplitude in different theory.

Propagators are consistent with known bulk Green's functions.

Abstract

We study the three-dimensional Carrollian field theory on the Rindler horizon which is dual to a bulk massless scalar field theory in the four-dimensional Rindler wedge. The Carrollian field theory could be mapped to a two-dimensional Euclidean field theory in the transverse plane by a Fourier transform. After defining the incoming and outgoing states at the future and past Rindler horizon, respectively, we construct the boundary-to-boundary and bulk-to-boundary propagators that are consistent with the bulk Green's function in the literature. We investigate the tree-level Carrollian amplitudes up to four points. The tree-level four-point Carrollian amplitude in $\Phi^4$ theory has the same structure as the one-loop triangle Feynman integral in the Lee-Pomeransky representation with complex powers in the propagators and spacetime dimension. Moreover, the four-point Carrollian amplitude with a zero energy state inserted at infinity in $\Phi^4$ theory is proportional to the three-point Carrollian amplitude in $\Phi^3$ theory.