Feynman rules and loop structure of Carrollian amplitudes

• Published in: The journal of high energy physics Vol. 2024; no. 5; pp. 213 - 66
• Main Authors: Liu, Wen-Bin, Long, Jiang, Ye, Xiao-Quan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 17.05.2024; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Celestial sphere; Classical and Quantum Gravitation; Duality in Gauge Field Theories; Elementary Particles; Fourier transforms; Physics; Physics and Astronomy; Polynomials; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Renormalization and Regularization; Scattering amplitude; String Theory; Duality in Gauge Field Theories; AdS-CFT Correspondence; Renormalization and Regularization
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2024)213

A bstract In this paper, we derive the Carrollian amplitude in the framework of bulk reduction. The Carrollian amplitude is shown to relate to the scattering amplitude by a Fourier transform in this method. We propose Feynman rules to calculate the Carrollian amplitude where the Fourier transforms emerge as the integral representation of the external lines in the Carrollian space. Then we study the four-point Carrollian amplitude at loop level in massless Φ 4 theory. As a consequence of Poincaré invariance, the four-point Carrollian amplitude can be transformed to the amplitude that only depends on the cross ratio z of the celestial sphere and a variable χ invariant under translation. The four-point Carrollian amplitude is a polynomial of the two-point Carrollian amplitude whose argument is replaced with χ . The coefficients of the polynomial have branch cuts in the complex z plane. We also show that the renormalized Carrollian amplitude obeys the Callan-Symanzik equation. Moreover, we initiate a generalized Φ 4 theory by designing the Feynman rules for more general Carrollian amplitude.