Year of Graduation
Level of Access
Restricted Access Thesis
Department or Program
Physics and Astronomy
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.
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