<p>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<sup>4</sup> 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<sup>4</sup> theory is proportional to the three-point Carrollian amplitude in Φ<sup>3</sup> theory.</p>

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Carrollian propagator and amplitude in Rindler spacetime

  • Ang Li,
  • Jiang Long,
  • Jing-Long Yang

摘要

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 Φ4 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 Φ4 theory is proportional to the three-point Carrollian amplitude in Φ3 theory.