Description
- Abstract:
- In this thesis, we present studies of the structures of loop-level amplitudes in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory, via tensor diagrams and hyperbolic volumes, and singularity of scattering amplitudes in Yang-Mills and gravity from the celestial perspective. First, we propose to use tensor diagrams and the Fomin-Pylyavskyy conjectures to explore the connection between symbol alphabets of $n$-particle amplitudes in planar $\mathcal{N} = 4$ super Yang-Mills theory and certain polytopes associated to the Grassmannian $G(4, n)$. We show how to assign a web (a planar tensor diagram) to each facet of these polytopes. These web diagrams encode all known rational letters, and all square roots of the known algebraic letters up to $n=9$. Second, we provide an explicit analytic result for the one-loop scalar $n$-gon Feynman integral in $n$ dimensions, for even $n$, with massless or massive internal and external edges. The result can be represented by the volume of a hyperbolic object called orthoscheme. Furthermore, we evaluate the general six-dimensional hexagon integral in terms of classical polylogarithms. Finally, we show that associativity of the tree-level OPE in a celestial CFT imposes constraints on the coupling constants of the corresponding bulk theory. The constrained theories are interesting as apparently well-defined celestial CFTs with a deformed $w_{1+\infty}$ symmetry algebra. We explicitly work out the ramifications of these constraints on scattering amplitudes and find that all $n$-point amplitudes constructible solely from holomorphic or anti-holomorphic three-point amplitudes vanish on the support of these constraints. We then studied the regular terms of the OPE of MHV amplitudes and the partial differential equations the MHV celestial amplitudes should satisfy. These PDEs originate from BCFW recursion of bulk amplitudes. We also investigate further structures of the celestial dual of planar $\mathcal{N}=4$ SYM theory from dual superconformal symmetry.
- Notes:
- Thesis (Ph. D.)--Brown University, 2024
Citation
Ren, Lecheng,
"Aspects of Scattering Amplitudes: Tensor Diagrams, Hyperbolic Volumes, and Celestial Sphere"
(2024).
Physics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://repository.library.brown.edu/studio/item/bdr:dhbeqagf/
