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Title: Group symmetries and the moduli space structures of SUSY quiver gauge theories
Author: Kalveks, Rudolph
ISNI:       0000 0004 6422 7669
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2017
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This thesis takes steps towards the development of a systematic account of the relationships between SUSY quiver gauge theories and the structures of their moduli spaces. Highest Weight Generating functions (“HWGs”), which concisely encode the field content of a moduli space, are introduced and developed to augment the established plethystic techniques for the construction and analysis of Hilbert series (“HS”). HWGs are shown to provide a faithful means of decoding and describing HS in terms of their component fields, which transform in representations of Classical and/or Exceptional symmetry groups. These techniques are illustrated in the context of Higgs branch quiver theories for SQCD and instanton moduli spaces, as a prelude to an account of the quiver theory constructions for the canonical class of moduli spaces represented by the nilpotent orbits of Classical and Exceptional symmetry groups. The known Higgs and/or Coulomb branch quiver theory constructions for nilpotent orbits are systematically extended to give a complete set of Higgs branch quiver theories for Classical group nilpotent orbits and a set of Coulomb branch constructions for near to minimal orbits of Classical and Exceptional groups. A localisation formula (“NOL Formula”) for the normal nilpotent orbits of Classical and Exceptional groups based on their Characteristics is proposed and deployed. Dualities and other relationships between quiver theories, including A series 3d mirror symmetry, are analysed and discussed. The use of nilpotent orbits, for example in the form of T(G) quiver theories, as building blocks for the systematic (de)construction of moduli spaces is illustrated. The roles of orthogonal bases, such as characters and Hall Littlewood polynomials, in providing canonical structures for the the analysis of quiver theories is demonstrated, along with their potential use as building blocks for more general families of quiver theories.
Supervisor: Hanany, Amihay Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral