Pure & Applied Mathematics (Theses and Dissertations)
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Duality and domains in supersymmetric gauge theories
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)This thesis investigates duality properties of fourdimensional N = 2 supersymmetric YangMills theory. By restricting the domain of the effective coupling to an appropriate fundamental domain the order parameter on the ... 
Modularity in Supersymmetric Gauge Theory
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)In this thesis, we study the modularity and duality of Coulomb branches for a class of fourdimensional N=2 supersymmetric gauge theories. For pure N=2 super YangMills theory with gauge group SU(2), the Coulomb branch can ... 
Conformal Bootstrap and Black Holes in AdS/CFT
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)In this thesis, we explore applications of the conformal bootstrap to holographic CFTs that are dual to theories of gravity in asymptotically Antide Sitter spacetimes. In particular, we consider correlation functions with ... 
Automorphic Symmetries, String integrable structures and Deformations
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)We address the novel structures arising in quantum and string integrable theories, as well as construct methods to obtain them and provide further analysis. Specifically, we implement the automorphic symmetries on ... 
Coherent states and classical radiative observables in the Smatrix formalism
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)In this thesis, we study classical radiative observables perturbatively in terms of onshell scattering amplitudes. In particular, we focus primarily on the twobody problem in gauge and gravitational theories by using an ...