Bibliography : leaves 117-120 / vi, 120 leaves ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1992

Title page, contents and abstract only. The complete thesis in print form is available from the University of Adelaide Library. / In this thesis we present a comprehensive study of perturbative and non-perturbative non-Abelian gauge theories in the light of gauge-fixing procedures, focusing our attention on the BRST formalism in Yang-Mills theory. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1284180 / Thesis (Ph.D.) -- University of Adelaide, School of Chemistry and Physics, 2007

Thesis (Ph. D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1992. / Includes bibliographical references (p. 105-111).

Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 2002. / Bibliography: leaves 124-127.

Thesis (Ph.D.)--University of Adelaide, School of Chemistry and Physics, Discipline of Physics, 2004. / Bibliography: p. 222-229.

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In this thesis we study two classes of backgrounds in Typo IIB supergravity which admit interpretation in terms of dual N = 1 Supersymmetric Field Theories. The first is obtained by wrapping D5 branes on a two-cycle inside the conifold; the second is the class containing the dual to the baryonic branch of Klebanov-Strassler. These backgrounds are related via a 'solution generating procedure' (or rotation) and have a number of interesting properties. First, we study non-Supersymmetric deformations of the baryonic branch by making use of the rotation procedure. We interpret these deformations as soft-breaking through the addition of gaugino masses, and calculate various observables which support this picture. We then explore the two-dimensional solution space of supergravity solutions associated with these deformations, finding a number of interesting limiting cases. We see that much of the structure of the Supersymmetric baryonic branch survives, even for large values of the deformation. Second, we study probe-D7 branes which wrap an internal three-dimensional manifold and lie at the equator of the transverse two-sphere, in the class of wrapped D5 brane backgrounds. We employ this method to model Chiral-symmetry breaking and present a simple diagnostic tool for determining the classical stability of such embeddings, in particular cases we find that a new type of phase transition appears, putting limits on the region of parameter space which can be used to study physics of the dual field theory. Finally, we study the relationship between confinement in a Quantum Field Theory and the presence of a first-order phase transition in its Entanglement Entropy. We determine the sufficient conditions for such a phase transition and compare to the conditions on a Rectangular Wilson Loop to probe confinement. In certain backgrounds with non-local high energy behaviour, we show that new configurations (associated with the introduction of a UV cutoff) are required in order to recover the otherwise absent phase transition. We also show that a local UV-completion, obtained using the rotation procedure, to the non-local theories has a similar effect to the cutoff.

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Fases topológicas da matéria são caracterizadas por terem uma degenerescên- cia do estado fundamental que depende da topologia da variedade em que o sistema físico é definido, além disso apresentam estados excitados no interior do sistema que são interpretados como sendo quase-partículas com estatística de tipo anyonica. Estes sistemas apresentam também excitações sem gap de energia em sua borda. Fases topologicamente ordenadas distintas não podem ser distinguidas pelo esquema usual de quebra de simetria de Ginzburg-Landau. Nesta dissertação apresentamos como exemplo o modelo mais simples de um sistema com Ordem Topológica, a saber, o Toric Code (TC), introduzido originalmente por A. Kitaev em [1]. O estado fundamental deste modelo ap- resenta degenerescência igual a 4 quando incorporado à superfície de um toro. As excitações elementares são interpretadas como sendo quase-partículas com estatística do tipo anyonica. O TC é um caso especial de uma classe mais geral de models chamados de Quantum Double Models (QDMs), estes modelos podem ser entendidos como sendo uma implementação de Teorias de gauge na rede em (2 + 1) dimensões na formulação Hamiltoniana, em que os graus de liberdade vivem nas arestas da rede e são elementos do grupo de gauge G. Nós generalizamos estes modelos com a inclusão de campos de matéria nos vértices da rede. Também apresentamos uma construção detalhada de tais modelos e mostramos que eles são exatamente solúveis. Em particular, exploramos o modelo que corresponde à escolher o grupo de gauge como sendo o grupo cíclico Z2 e os graus de liberdade de matéria como sendo elementos de um espaço vetorial bidimensional V2. Além disso, mostramos que a degenerescência do estado fundamental não depende da topologia da variedade e obtemos os estados excitados mais elementares deste modelo. / Topological phases of matter are characterized for having a topologically dependent ground state degeneracy, anyonic quasi-particle bulk excitations and gapless edge excitations. Different topologically ordered phases of matter can not be distinguished by te usual Ginzburg-Landau scheme of symmetry breaking. Therefore, a new mathematical framework for the study of such phases is needed. In this dissertation we present the simplest example of a topologically ordered system, namely, the \\Toric Code (TC) introduced by A. Kitaev in [1]. Its ground state is 4-fold degenerate when embedded on the surface of a torus and its elementary excited states are interpreted as quasi-particle anyons. The TC is a particular case of a more general class of lattice models known as Quantum Double Models (QDMs) which can be interpreted as an implementation of (2+1) Lattice Gauge Theories in the Hamiltonian formulation with discrete gauge group G. We generalize these models by the inclusion of matter fields at the vertices of the lattice. We give a detailed construction of such models, we show they are exactly solvable and explore the case when the gauge group is set to be the abelian Z_2 cyclic group and the matter degrees of freedom to be elements of a 2-dimensional vector space V_2. Furthermore, we show that the ground state degeneracy is not topologically dependent and obtain the most elementary excited states.

The objective of this Thesis is to explore Poincaré Gauge theories of gravity and expose some contributions to this field, which are detailed below. Moreover, a novel ultraviolet non-local extension of this theory shall be provided, and it will be shown that it can be ghost- and singularity-free at the linear level. First, we introduce some fundamentals of differential geometry, base of any gravitational theory. We then establish that the affine structure and the metric of the spacetime are not generally related, and that there is no physical reason to impose a certain affine connection to the gravitational theory. We review the importance of gauge symmetries in Physics and construct the quadratic Lagrangian of Poincaré Gauge gravity by requiring that the gravitational theorymust be invariant under local Poincaré transformations. We study the stability of the quadratic Poincaré Gauge Lagrangian, and prove that only the two scalar degrees of freedom (one scalar and one pseudo-scalar) can propagate without introducing pathologies. We provide extensive details on the scalar, pseudo-scalar, and bi-scalar theories. Moreover, we suggest how to extend the quadratic Poincaré Gauge Lagrangian so that more modes can propagate safely. We then proceed to explore some interesting phenomenology of Poincaré Gauge theories. Herein, we calculate how fermionic particles move in spacetimes endowed with a nonsymmetric connection at first order in the WKB approximation. Afterwards, we use this result in a particular black-hole solution of Poincaré Gauge gravity, showing that measurable differences between the trajectories of a fermion and a boson can be observed. Motivated by this fact, we studied the singularity theorems in theories with torsion, to see if this non-geodesical behaviour can lead to the avoidance of singularities. Nevertheless, we prove that this is not possible provided that the conditions for the appearance of black holes of any co-dimension are met. In order to see which kind Black Hole solutions we can expect in Poincaré Gauge theories, we study Birkhoff and no-hair theorems under physically relevant conditions. Finally, we propose an ultraviolet extension of Poincaré Gauge theories by introducing non-local (infinite derivatives) terms into the action, which can ameliorate the singular behaviour at large energies. We find solutions of this theory at the linear level, and prove that such solutions are ghost- and singularity-free. We also find new features that are not present in metric Infinite Derivative Gravity.