Topics in Quiver Gauge Theories

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The data of certain supersymmetric gauge theories can be contained in a diagram called a quiver. We aim to study the moduli space (of vacua) of various quiver gauge theories in different dimensions and with various amounts of supersymmetry.The Hilbert series of Higgs and Coulomb branches of quiver gauge theories allow us to understand the gauge invariant operators that parameterise these moduli spaces. These are often algebraic varieties such as (closures of) nilpotent orbits of classical and exceptional algebras. This has been interesting for both physicists and mathematicians. Computations of Hilbert series for Higgs and Coulomb branches of various quiver gauge theories and interpreting physics or mathematics from these would be a large focus of the project.The dynamics of quiver gauge theories can be realised using the brane construction from string theory. Duality symmetries such as 3d mirror symmetry, for example, are realised as branes and relate the Higgs and Coulomb branches of a quiver gauge theory. It would be a goal for this project, to better understand certain quiver gauge theories as a brane system.