UNIVERSITY of CALIFORNIA Los Angeles Modern Applications Of
UNIVERSITY OF CALIFORNIA Los Angeles Modern Applications of Scattering Amplitudes and Topological Phases A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Physics by Julio Parra Martinez 2020 © Copyright by Julio Parra Martinez 2020 ABSTRACT OF THE DISSERTATION Modern Applications of Scattering Amplitudes and Topological Phases by Julio Parra Martinez Doctor of Philosophy in Physics University of California, Los Angeles, 2020 Professor Zvi Bern, Chair In this dissertation we discuss some novel applications of the methods of scattering ampli- tudes and topological phases. First, we describe on-shell tools to calculate anomalous dimen- sions in effective field theories with higer-dimension operators. Using such tools we prove and apply a new perturbative non-renormalization theorem, and we explore the structure of the two-loop anomalous dimension matrix of dimension-six operators in the Standard Model Ef- fective Theory (SMEFT). Second, we introduce new methods to calculate the classical limit of gravitational scattering amplitudes. Using these methods, in conjunction with eikonal techniques, we calculate the classical gravitational deflection angle of massive and massles particles in a variety of theories, which reveal graviton dominance beyond 't Hooft's. Finally, we point out that different choices of Gliozzi-Scherk-Olive (GSO) projections in superstring theory can be conveniently understood by the inclusion of fermionic invertible topological phases, or equivalently topological superconductors, on the worldsheet. We explain how the classification of fermionic topological phases, recently achieved by the condensed matter community, provides a complete and systematic classification of ten-dimensional superstrings and gives a new perspective on the K-theoretic classification of D-branes.
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