From Building Blocks to Theories: EFThedron and a Haagerup TFT

Citation

Huang, Tzu-Chen (2022) From Building Blocks to Theories: EFThedron and a Haagerup TFT. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7yyr-rb39. https://resolver.caltech.edu/CaltechTHESIS:05262022-082058996

Abstract

This thesis is dedicated to the study of certain building blocks of scattering amplitudes in (3+1)d Minkowskian spacetime and that of topological field theory in (1+1)d, together with the constraints which result from the properties of these building blocks.

The first part of the thesis is concerned with the introduction of an on-shell formalism for massless and massive particles. We identify all possible three-point tensor structures compatible with the little group symmetry and overall mass dimension, and use them to arrive at a new description of various scattering amplitudes through unitarity and locality. One of the objects that result from this construction, the spinning polynomial, is then fed into the dispersion relation to derive a convex hull constraining the EFT coefficients. We further investigate the intersection of the convex hull resulting from the positive expansion of residue and the half moment curve.

In the second part, we turn our attention to topological defect lines in (1+1)d topological field theory with Haagerup fusion ring. We first solve for the F-symbols of fusion categories in the Haagerup-Izumi family under the assumption of transparency. The purpose of transparency is twofold: it allows for a simple formula for F-symbols while at the same time tremendously simplifies the diagrammatic calculus with topological defect lines. Finally, we construct a topological field theory with 15 pointlike operators and demonstrate that it satisfies the four-point crossing constraints and torus one-point modular invariance constraints.

Thesis Files