Ph.D. Theses
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Browsing Ph.D. Theses by Author "Bleeken, Dieter Van den."
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Item Adiabatic solutions in general relativity and boundary symmetries(Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2020., 2020.) Kutluk, Emine Şeyma.; Bleeken, Dieter Van den.We investigate adiabatic solutions to general relativity for a spacetime with spatial slices with boundary, by Manton approximation. This approximation tells us for a theory with a Lagrangian in the natural form, a motion that is described as a slow motion on the space of vacua-static solutions that minimize the energy- is a good approximate solution. To apply this to the case of general relativity we rst bring it to the natural form by splitting space and time and choosing Gaussian normal coordinates, where a spacetime is described by the metric on its spatial slices. Then following Manton we propose slow solutions such that each slice is a slowly changing di eomorphism of a reference slice, and thus each solution is described by a vector eld on the spatial slice. These solutions will have the property that the action will become a functional of the vector elds on the boundaries of the spatial slices. Moreover using the Hodge- Morrey-Friedrichs decomposition we will show that the constraints of general relativity will identify a unique solution for a given boundary value. Then we comment on the structure of the space of vacua which we show to be a (pseudo)-Riemannian homogeneous space. We illustrate our procedure for a speci c reference slice we choose: the 3d Euclidean round ball.Item On BPS dyons in N = 2 supersymmetric theories(Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2023., 2023) Şanlı, Canberk.; Bleeken, Dieter Van den.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.Item Perturbative and non-perturbative physics from singularities(Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022), 2022) Pazarbaşı, Cihan.; Bleeken, Dieter Van den.A function that representing a physical quantity has singularities which con tain perturbative or non-perturbative information about the physical system under investigation. Moreover, the theory of resurgence tells us that these perturbative and non-perturbative parts are intimately connected and it is possible to use one of them to obtain the other one. In this thesis, we combine these two ideas with a focus on the functions formulated in integral representations. Specifically, first consider ing two different examples on the semi-classical expansion in quantum mechanics and the pair production problem in electromagnetic backgrounds, we will concentrate on the quantum action which we express in the Schwinger’s integral representation. We will show that the perturbative and non-perturbative information about the physical system is hidden in singularities of the propagator TrU(t). The way we obtain the non-perturbative one is very similar to the Borel method which is used to handle the divergent perturbation series. Contrary to the Borel method, by probing the singular ities of TrU(t) directly and using the iε prescription, we will be able to prevent the Borel ambiguity problem in the physical cases that it leads to the violation of the uni tarity. Later, we will turn our attention to the renormalon problem in non-relativistic quantum mechanics. After presenting the existence of the renormalon divergence in a scattering problem with a background potential consisting of 2D δ-potential perturbed with a tilted 1D δ-potential, we will argue that the Borel ambiguity in the summation of the divergent series can be prevented again by a careful application of the iε pre scription and the resulting non- perturbative contribution due to the renormalon obeys the causality condition.Item Scaling solutions of N = 2 supergravity and holography(Thesis (Ph.D.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2019., 2019.) Mirfendereski, Delaram.; Bleeken, Dieter Van den.The 4D N = 2 SUGRA is the low energy limit of Type II string theory compactified on a Calabi-Yau three-fold. The theory contains BPS black holes with multi centered configurations consisting of bound states of dyonic single-centered black holes. These stationary solutions have an intrinsic angular momentum originating in electro magnetic interaction between charges. A subset of this family called “scaling solutions” for which the relative distances between centers are constrained up to a scale. Contrary to the asymptotically flat non-scaling cases, scaling solutions have an AdS2 factor in their asymptotic geometry and their total angular momentum vanishes. We showed that the AdS2 spacetime at far infinity is equipped with an S2 fiber called a “twist”. It can be thought of as a rotating two-sphere whose angular velocity is determined by the total charge and the total dipole moment of the black hole. In the absence of an angular momentum, the twist can be considered as a topological hair of this family of supersymmetric black holes. It provides a new asymptotic observable to distinguish different black hole solutions. Moreover, to have a better understanding of the twist and its potential role in a quantum theory of supersymmetric black holes, we S2 reduced the asymptotic geometry of the scaling solutions. That leads to an effective 2D theory with an AdS2 geometry and a single U(1) gauge field presenting the twist. Consequently, one would expect the AdS/CFT correspondence to clarify the role of the twist as a new hair of these black holes.