UCLA

In this dissertation we discuss some novel applications of the methods of

scattering amplitudes and topological phases. First, we describe on-shell tools

to calculate anomalous dimensions 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 Effective 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.