Benefits of Supersymmetry: From Scattering Amplitudes to Higher-Spin Gravity.

Abstract

In this dissertation, we study two topics related to supersymmetry. One topic is the computation of scattering amplitudes in supersymmetric Yang-Mills (SYM) theory via on-shell methods. We develop a formalism to compute the SYM scattering amplitudes with N<4 supersymmetries and examine various properties of the results. In particular, with the help of the generalized unitarity method, we identify the origin of the 1-loop UV divergence of the N<4 SYM amplitudes. The second topic is on higher-spin gravity in 3-dimensional anti-de Sitter spacetime. We find a noval generalization of higher-spin gravity that includes supersymmetry in the framework of the gauge/gravity correspondence. By explicit computation, we match the asymptotic symmetry of the higher-spin supergravity with the chiral symmetry of the 't Hooft limit of the CP^n model, which is the proposed dual 2-dimensional conformal field theory (CFT). In addition, we consider the special case of spin-3 supergravity and find 3 distinct vacua. We find renormalization group (RG) flows connecting two of them to the third vacuum. Thus a new duality between the two ultraviolet (UV) theories emerges in the sense that the two theories flow to the same infrared (IR) theory. We also match this with a similar duality structure in the dual CFT, which comes from the Hamiltonian reductions of the 2-dimensional Wess-Zumino-Witten (WZW) model.