Relations between four-point amplitudes in N=4 supersymmetric Yang-Mills theory and N=8 supergravity at one, two, and three loops

Author

Theodore Wolcott Wecker, Bowdoin CollegeFollow

Year of Graduation

2022

Level of Access

Restricted Access Thesis

Embargo Period

5-19-2022

Department or Program

Physics and Astronomy

First Advisor

Stephen Naculich

Abstract

This honors paper considers the 2-to-2 scattering process in two models, N=4 supersymmetric Yang-Mills Theory (SYM) and N=8 supergravity, and searches to identify relations between them. The motivation for doing so is a conjecture posed for a relation between N=4 SYM and N=8 supergravity three-loop four-point amplitudes in the Regge limit. In order to verify this conjecture, the analogous exact relations are first proven at the one and two-loop levels.

First, four-momenta of interacting particles are rigorously defined and group theory relations in both color factors and scalar integrals are identified. These results are then used to calculate N=4 SYM four-point color-ordered amplitudes, before relating them to the analogous four-point amplitude given by N=8 supergravity. In the one and two-loop cases exact relations are re-derived and presented.

In the three-loop case, the conjectured Regge limit relation is expanded upon by calculating and applying the three-loop N=4 SYM color-ordered amplitudes. Additionally, an exact relation is searched for at three loops. These results have been incorporated into [https://doi.org/10.48550/arXiv.2204.02417], where the proofs are continued.