RSS 1.0School of Mathematics
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Pure & Applied Mathematics
Pure & Applied Mathematics
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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 four-dimensional N = 2 supersymmetric Yang-Mills 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 four-dimensional N=2 supersymmetric gauge theories. For pure N=2 super Yang-Mills 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 Anti-de 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 ... -
Characters, coadjoint orbits and Duistermaat-Heckman integrals
(2021)The asymptotics of characters of irreducible representations of a compact Lie group G for large values of the scaling factor k are given by Duistermaat-Heckman (DH) integrals over coadjoint orbits of G. This phenomenon ...
