ABJM Scattering Amplitudes & Duality Test in Higher-Dimensional SCFTs

Abstract

This dissertation consists of two parts. In the first part, I discuss about ABJM scattering amplitudes. I develop a new gauge choice for the orthogonal Grassmannian formulation of ABJM amplitudes called u-gauge. Using the u- gauge choice, I compute 8-point ABJM amplitude for a first time. I also derive an ABJM soft theorem via the recursion relation for ABJM amplitudes. In the second part, I study UV dualities between higher-dimensional SCFTs by com- paring their supersymmetric indices. More concretely, I focus on the UV duality between 5d N = 1 SU(3) with Nf = 10 fundamental hypermultiplets and 5d N = 1 Sp(2) gauge theory with same number of hypermultiplets. Furthermore, I study the index of their conjectured UV SCFT which is 6d N = (1, 0) SCFT on a circle with Sp(1) gauge symmetry and Nf = 10 fundamental hypermulti- plets. Instantons play an important role in the duality, and string theory gives a nice way of the ADHM construction for the super-Yang-Mills theories.