Topics in quiver gauge theories

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The student will study the formulation and broad applications of quiver gauge theories. These form a large class of quantum field theories, usually required to have additional supersymmetry and existing in diverse spacetime dimensions. Their dynamics can be interpreted by embedding their degrees of freedom in string theory, using extended "brane" states. Supersymmetry constrains the geometry of the resulting moduli spaces (of vacua) and so gives important new constructions and interpretations of certain classic geometries, notably hyper-Kahler spaces, including particular classes of singularities. This has provided an extremely rich source of research in both physics and mathematics. Two central ideas in the constructions are the role of duality symmetries, relating apparently distinct theories with different symmetries, and the notion of brane transitions connecting different sectors of moduli space. The project will focus on a range of quiver theory constructions in different spacetime dimensions and degree of supersymmetry, with different gauge groups and global symmetries.