On BPS dyons in N = 2 supersymmetric theories
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Date
2023
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Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2023.
Abstract
N = 4 superconformal mechanics of the (3, 4, 1) multiplet describes the scaling limit of the effective Coulomb quiver mechanics. There is an equivalent hyperK¨ahler with torsion (HKT) gauged sigma model (4, 4, 0) reformulation which becomes equivalent to the original (3, 4, 1) formulation (only) on the quotient spaceM/G whereMis the HKT target space of the gauged model and G is the group of (gauged) isometries of M. This opens a genuinely new class of superconformal mechanical models not explored before. We systematically study N = 0, 1, 2 supersymmetric analogs as well. These gauged sigma models are only scale invariant before gauging, and become (super) conformally invariant after gauging. We obtain these results by explicitly checking the superconformal invariance of the Lagrangian which gives the conformal geometry constraints and by checking the superconformal algebra satisfied by the Noether charges which provide additional constraints. For the N = 2, 4 gauged sigma models, we obtain a differential geometric description for the prequantum Hilbert space, and discuss the applications of our work to the pure AdS2/CFT1 duality. There is a well-known self-dual formulation of point dyons in classical electromagnetism. Starting from Dirac’s original theory of monopoles, we obtain a particularly useful self-dual reformulation, and employ it to describe the coupling of BPS point dyons to N = 2, d = 4 low energy effective actions which in particular recovers Denef’s core-halo description for BPS bound states but also allows for certain generalizations when the bound state radius becomes small as one approaches to the Higgs phase. We explain how these two descriptions for N = 2 BPS (bound) states, as well as various other faces of them, obtain a unified view in the context of quiver (quantum) mechanics. NOTE Keywords : Lie symmetries, Conformal symmetry, Black holes, Quantum field theory, Effective field theories, Conformal invariant field theories, Supersymmetry, Effective string theory, Quiver theory, Superconformal algebras.