UC Santa Barbara

The functional form of the $S$-matrix is heavily constrained by both causality and unitarity to the extent to which it may be substantially reconstructed without computational recourse to a field-theoretic action, thereby avoiding complications arising from gauge fixing and field-variable redundancy. In this context, simplifications provided by supersymmetric theories have been fruitful in guiding these methods and enabling perturbatively deeper computations.

In this thesis, on-shell, unitarity-based $S$-matrix methods are generalised to supersymmetric theories of massive particles. An on-shell superspace for massive supermutiplets is developed and used to classify all three-particle interactions consistent with supersymmetry in gauge theories in four dimensions. In $\mathcal{N}=4$ super-Yang-Mills theory, this is used to compute scattering amplitudes for BPS particles using on-shell recursion.

The impact of causality on the contact couplings parameterising effective theories are then considered. Dispersion relations are used to constrain the space of these couplings for several simple interactions relevant to extensions of the Standard Model of particle physics. It is shown how these bounds unify as components of the same constraint under supersymmetry.

Finally, as the observable world lacks supersymmetry, a possible intermediary extension of the Standard Model called the Twin Higgs, bridging a minor hierarchy of scales between the Higgs potential and a UV completion, is considered. In particular, the impact of numerous new, light, invisible particles on the spectrum of temperature anisotropies of the Cosmic Microwave Background is calculated as a function of the twin electroweak scale. The observable impact of a possible dilution of the twin particles relative to their Standard Model counterparts by the decay of a particle reheating the universe is then projected.