Carrollian propagator and amplitude in Rindler spacetime

Fuente: arXiv
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Main Authors: Li, Ang, Long, Jiang, Yang, Jing-Long
Format: Preprint
Published: 2024
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author Li, Ang
Long, Jiang
Yang, Jing-Long
author_facet Li, Ang
Long, Jiang
Yang, Jing-Long
contents 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 $Φ^4$ 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 $Φ^4$ theory is proportional to the three-point Carrollian amplitude in $Φ^3$ theory.
format Preprint
id arxiv_https___arxiv_org_abs_2410_20372
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Carrollian propagator and amplitude in Rindler spacetime
Li, Ang
Long, Jiang
Yang, Jing-Long
High Energy Physics - Theory
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 $Φ^4$ 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 $Φ^4$ theory is proportional to the three-point Carrollian amplitude in $Φ^3$ theory.
title Carrollian propagator and amplitude in Rindler spacetime
topic High Energy Physics - Theory
url https://arxiv.org/abs/2410.20372