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Title: On classical and quantum moduli spaces of supersymmetric gauge theories
Author: Ferlito, Giulia
ISNI:       0000 0004 7657 8802
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2018
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This manuscript presents some results that concern supersymmetric theories with eight supercharges and moduli spaces of instantons. The latter are attacked from two fronts. Firstly we study the quantum-corrected Coulomb branch of three-dimensional N = 4 quiver theories which are encoded in the over-extended Dynkin diagram of a group G. Studying the ring of gauge invariant operators on the Coulomb branch for these theories by means of a generalised monopole formula yields precisely the Hilbert series for the moduli space of G-instantons. We provide results for any G, including non-simply-laced and exceptional groups. In the second part of the thesis we analyse the Higgs branch of some five-dimensional N = 1 supersymmetric gauge theories. We provide a description of the quantum-corrected Higgs branch in terms of instanton operators, the glueball superfield and mesons. In particular, a classical nilpotent relation is found to be corrected by bilinears in instanton operators. The analysis depends on a decomposition of the Hilbert series for the moduli space of E_{N_f +1} instantons into SO(2Nf) instantons, which are the known Higgs branch at infinite and finite coupling respectively. The dressing of instanton operators in terms of finite coupling fields is also analysed. In passing, we also present an interesting phenomenon where the Higgs branch of a given family of gauge theories with eight supercharges and classical gauge and global symmetry groups is not a single hyperKähler cone but rather the union of two such cones with nontrivial intersection.
Supervisor: Hanany, Amihay Sponsor: Science and Technology Facilities Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral