Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (p. 92-96).

Thesis is submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the University of the Witwatersrand, Faculty of Science, School of Physics, University of the Witwatersrand, Johannesburg, 2018 / Like any field or topic of research, significant advancements can be made with increasing computational power - string theory is no exception. In this thesis, an analysis is performed within three areas: Calabi–Yau manifolds, cosmological inflation and application of conformal field theory. Critical superstring theory is a ten dimensional theory. Four of the dimensions refer to the spacetime dimensions we see in nature. To account for the remaining six, Calabi-Yau manifolds are used. Knowing how the space of Calabi-Yau manifolds is distributed gives valuable insight into the compactification process. Using computational modeling and statistical analysis, previously unseen patterns of the distribution of the Hodge numbers are found. In particular, patterns in frequencies exhibit striking new patterns - pseudo-Voigt and Planckian distributions with high confidence and exact fits for many substructures. The patterns indicate typicality within the landscape of Calabi–Yau manifolds of various dimensions. Inflation describes the exponential expansion of the universe after the Big Bang. Finding a successful theory of inflation centres around building a potential of the inflationary field, such that it satisfies the slow-roll conditions. The numerous ways this can be done, coupled with the fact that each model is highly sensitive to initial conditions, means an analytic approach is often not feasible. To bypass this, a statistical analysis of a landscape of thousands of random single and multifield polynomial potentials is performed. Investigation of the single field case illustrates a window in which the potentials satisfy the slow-roll conditions. When there are two scalar fields, it is found that the probability depends on the choice of distribution for the coefficients. A uniform distribution yields a 0.05% probability of finding a suitable minimum in the random potential whereas a maximum entropy distribution yields a 0.1% probability. The benefit of developing computational tools extends into the interdisciplinary study between conformal field theory and the theory of how wildfires propagate. Using the two dimensional Ising model as a basis of inspiration, computational methods of analyzing how fires propagate provide a new tool set which aids in the process of both modeling large scale wildfires as well as describing the emergent scale invariant structure of these fires. By computing the two point and three point correlations of fire occurrences in particular regions within Botswana and Kazakhstan, it is shown that this proposed model gives excellent fits, with the model amplitude being directly proportional to the total burn area of a particular year. / EM2018

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2016. / The convenient pictorial descriptions of the half-BPS and near-BPS sectors of the AdS=CFT equivalent theories of N = 4, D = 4 super Yang-Mills and D = 10 Type IIB superstring theory on AdS5 S5 are exploited in this thesis by using Schur polynomials labelled by Young diagrams as a basis for the gauge invariant operators in the eld theory. We use a \Fourier transform" on these operators to construct asymptotic eigenstates of the dilatation operator, the spectrum of which agrees precisely with the rst two leading order terms in the smallcoupling expansion of the exact result determined by symmetry. Motivated by the geometric description of the systems of open strings with magnon excitations to which the operators are dual, we propose a simple and minimal all-loop expression that interpolates between anomalous dimensions computed in the gauge theory and energies computed in the string theory. The connection to the string theory result provides the insight necessary to understand the interpretation of our Gauss graphs in the magnon language. Symmetry determines the two-body scattering matrix for the magnons up to a phase, and it is demonstrated that integrability is spoiled by the boundary conditions on the open strings. The Schur polynomial construction is then applied to the study of closed strings on a class of half- BPS excitations of the AdS5 S5 background. The string theory predictions for the magnon energies are again reproduced by calculating the anomalous dimensions of particular linear combinations of our operators. Group theoretic quantities which can be read o the Young diagram labels provide the correct modi cation of terms in the dilatation action to account for the energies of magnons at di erent radii on the LLM plane. The representation theory implies a natural splitting of the full symmetry group - the distinction between what is the background and what is the excitation is accomplished in the choice of the subgroup and representations used to construct the operator. Connecting the descriptions utilised in obtaining these results is expected to allow the construction of operators dual to general open string con gurations on the class of backgrounds considered. / GR 2016

Bibliography: leaves 181-190. This thesis firstly investigates K-invariant and supersymmetric actions of D-branes in curved space-time. Following this, research into charges of D-branes in a group manifold are studied. In particular, the charge groups are determined for the symmetry preserving (or untwisted) D-branes on a compact, simple, connected, simply connected group manifold. The purpose of this research is to determine these charge groups in order that they can be compared to the charge groups predicted by twisted K-theory for D-branes in a group manifold, thus providing a future important check to the theorem that D-brane charges are determined by twisted K-theory, one of the most important recent ideas in string theory.

Bibliography: leaves 181-190. / 190 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis firstly investigates K-invariant and supersymmetric actions of D-branes in curved space-time. Following this, research into charges of D-branes in a group manifold are studied. In particular, the charge groups are determined for the symmetry preserving (or untwisted) D-branes on a compact, simple, connected, simply connected group manifold. The purpose of this research is to determine these charge groups in order that they can be compared to the charge groups predicted by twisted K-theory for D-branes in a group manifold, thus providing a future important check to the theorem that D-brane charges are determined by twisted K-theory, one of the most important recent ideas in string theory. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 2003

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The object of this thesis is to present various applications of the theory of cosmological perturbations. Within are contained a number of manuscripts, each concerned with a separate aspect of the theory. The thesis itself begins with a general overview of cosmological perturbation theory designed to be accessible to the non-specialist. Both the classical and quantum first order theory are considered. Back-reaction, via the formalism of the Effective Energy Momentum Tensor (EEMT) is reviewed. Subsequent chapters are more specialized dealing with various applications of the theory. At first order, topics discussed include the classicalization of cosmological perturbations (chapter 2), and the effects of including the dilaton and its fluctuations on a novel mechanism for the production of inhomogeneities in string gas cosmology (chapter 3). At second order, an original solution to the Dark Energy problem is proposed (chapter 4), and the effects of back-reaction on the power spectrum, including the spectral index and the gaussianity, are examined (chapter 5).

A simple two scale compactification scheme for the E(8) x E(8) heterotic string is studied. The internal space used is a direct product of two compact spaces, each with its own length scale. Compactification on the smaller 4-dimensional (4d) manifold is carried out to obtain 6d theories with simple supersymmetry (SUSY). Assuming the background torsion vanishes, we show that this manifold must be K3. Compactification on K3 is studied in detail. Also analyzed are the two possible torsion-free compactifications on the orbifold K3$ sp prime$ (the limit of the manifold K3). The compactification from 6d to 4d on the larger scale 2d manifold results in Grand Unified Theories (GUT's) with broken SUSY. We show that it is not possible to generate a realistic theory using our scheme. Strings exclude what is conceivable from the perspective of point field theories: getting a realistic GUT from a 6d theory with simple SUSY.

Thesis (Ph.D.)--Tufts University, 2005. / Adviser: Alexander Vilenkin. Submitted to the Dept. of Physics and Astronomy. Includes bibliographical references (leaf 99). Access restricted to members of the Tufts University community. Also available via the World Wide Web;