Quiver Gauge Theory, String Theory and Quantum Field Theory.

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The student will study topics in quiver gauge theory and will attempt to expand the knowledge on this class of supersymmetric gauge theories with 8 supercharges.The techniques of quiver gauge theory have been used in recent years to better understand the geometry of the moduli space of various quantum gauge theories; Hasse diagrams, the monopole formula, quiver subtraction and addition, discrete gauging and hyper-Kähler quotients, and 3d mirror symmetry are some such examples.Quiver gauge theory also has important implications for mathematics - the language of quivers provides a different channel to probe geometric spaces and often offers a different perspective to the formal approach of the mathematician.In the past few years, quivers have been used to study gauge theories in, for example, three, five and six dimensions. In the associated brane setups, the Hanany-Witten transition is used to understand different phases and their associated physics. Current work includes extensions to the 'negative brane' setup in six dimensions, hyper-Kähler quotients and discrete gauging, expanding understanding of how the moduli spaces of different theories relate to each other.