Call number: LD2668 .T4 1957 M56 / Master of Science

<p>In this thesis we study aspects of (0,2) superconformal field theories (SCFTs), which are suitable for compactification of the heterotic string. In the first part, we study a class of (2,2) SCFTs obtained by fibering a Landau-Ginzburg (LG) orbifold CFT over a compact K\"ahler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model (GLSM), our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of GLSMs and comparing spectra among the phases. In the second part, we turn to the study of the role of accidental symmetries in two-dimensional (0,2) SCFTs obtained by RG flow from (0,2) LG theories. These accidental symmetries are ubiquitous, and, unlike in the case of (2,2) theories, their identification is key to correctly identifying the IR fixed point and its properties. We develop a number of tools that help to identify such accidental symmetries in the context of (0,2) LG models and provide a conjecture for a toric structure of the SCFT moduli space in a large class of models. In the final part, we study the stability of heterotic compactifications described by (0,2) GLSMs with respect to worldsheet instanton corrections to the space-time superpotential following the work of Beasley and Witten. We show that generic models elude the vanishing theorem proved there, and may not determine supersymmetric heterotic vacua. We then construct a subclass of GLSMs for which a vanishing theorem holds.</p> / Dissertation

A dissertation submitted to the faculty of science, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Master of Science. July 6, 2017. / We study the collective field theory of a free multi-matrix model in the radial sector, which has an emergent 1/r2 term, and take the large N limit. We show that it is possible to generate 2−d metrics with generic dependence on the collective field Lagrange multiplier (μ) and potential and which are distinguished by the choice of the potential. The Lagrange multiplier is shown to depend on an induced scale parameter after an I.R. regularization and breaks scale invariance. The collective field sl(2, R) algebras of the free Hamiltonian and a related alternative compact operator only close in the absence of μ. We point out that the broken conformal symmetry is contained in the associated metrics which suggests that they are related to a Near-AdS2 geometry. We also comment on the resemblance of these metrics to black hole solutions. / MT2018

A thesis submitted to the Faculty of Science, University of the Witwatersrand, in fulfilment of the requirements for the degree of Doctor of Philosophy February 2017. / In this dissertation we exploit the Ads slash CFT correspondence to describe a system of strings suspended between giant gravitons. The strings can be in an excited state. The excitations of the strings can be given a particle-like description and are known as magnons. The proposed gauge invariant operators used to construct a complete description of this system belong to the su(2) sector of the N = 4 SYM. Using an open spin chain description of the suspended strings, the states of the system we consider enjoy an SU 2j2)2 symmetry. By making use of this symmetry, we compute the all loop anomalous dimensions of these operators. The spectrum of the dilatation operator in the su(2) sector of the theory is reproduced in the dual gravity description. In the dual theory, the energies of the magnons are computed using strings in a background LLM geometry and the results are in complete agreement with the anomalous dimensions of the operators we have considered. Using the symmetries enjoyed by our system we achieve a complete determination - up to an overall phase - of the reection/scattering matrix between a boundary magnon and a bulk magnon. Thus, although the open boundary conditions of the spin chain spoil integrability. The two-loop subleading correction to the dilatation operator is also explored. This subleading term corresponds to a correction of the magnon energies. The computation of this subleading term requires consideration of the giant's backreaction on their excitations. We nd that this backreaction implies a nontrivial mixing of the dual operators and this mixing is characterized completely. / MT2017

One of the key goals of string theory is to provide a uni cation of general relativity and quantum eld theory. In the pursuit of this goal it has become clear that the di erent string theories that have been discovered so far are all in fact, partial descriptions of a single theory. At strong coupling a new theory, called M-theory, is the correct description. M-theory includes gravitons, M2-branes and M5-branes. Up to now, the correct description of the M5-brane is outstanding. In this project some proposals for this theory are studied. In particular, there is a proposal that D=5 maximally supersymmetric Yang-Mills theory can be used to provide a description of the world volume physics of the M5-brane. According to this proposal, instantons in D=5 maximally supersymmetric Yang-Mills theory are graviton excitations of the M theory. In this M.Sc dissertation the instanton solutions of D=5 maximally supersymmetric Yang-Mills theory are explored, with the goal of testing the above proposal. The dissertation begins with a review of the uses of instantons in quantum mechanics. In particular, instantons are used to account for tunneling e ects within a path integral approach to quantum mechanics. The lifting of ground state degeneracies as well as the estimation of the lifetime of unstable states using instantons is developed. The quantization of gauge theories is reviewed in detail. The relevance of instantons for a semi-classical study of Yang-Mills theory is explained. Finally, the relevance of instantons for D = 5 maximally supersymmetric Yang-Mills theory is considered.

MSc., Faculty of Science, University of the Witwatersrand, 2011 / Anomalous dimensions are calculated for a certain class of operators in the restricted Schur polynomial basis in the large N limit. A new computationally simple form of the dilatation operator is derived and used in this dissertation. The class of operators investigated have bare dimension of O(N). Thus the calculation necessarily sums non-planar Feynmann diagrams as the planar approximation has broken down for operators of this size. The operators investigated have two long columns and the operators mix under the action of the dilatation operator, however the mixing of operators having a different number of columns is suppressed and can be neglected in the large N limit. The action of the one loop dilatation operator is explicitly calculated for the cases where the operators have two, three and four impurities and it is found that in a particular limit the action of the one loop dilatation operator reduces to that of a discrete second derivative. The lattice on which the discretised second derivative is defined is provided by the Young tableaux itself. The one loop dilatation operator is diagonalised numerically and produces a surprisingly simple linear spectrum, with interesting degeneracies. The spectrum can be understood in terms of a collection of harmonic oscillators. The frequencies of the oscillators are all multiples of 8g2Y M and can be related to the set of Young tableaux acted upon by the dilatation operator. This equivalence to harmonic oscillators generalises on previously found results in the BPS sector, and suggests that the system is integrable. The work presented here is based primarily on research carried out by R.de Mello Koch, V De Comarmond, and K. Jefferies in [1].

Computational simulations of chemical systems play an ever-increasing role in many areas of biochemical research from rational drug design to probing fundamental physiological processes. Depending on the method, a vast array of properties are able to be predicted. Here we report the design and implementation of two methods for investigating diverse problems in protein biochemistry. In order to better understand protein–metal interactions—most importantly for the difficult to model transition metal ions— empirical force field parameters were developed for Pt(II), cisplatin, and other Pt(II) coordination compounds. Two force field frameworks were used: a modified version of the fixed- charge OPLS-AA and the polarizable POSSIM force field. A seven-site model was used for the Pt(II) ion. The produced parameters are compatible with the OPLS-AA and POSSIM force fields and can be used in protein–metal binding simulations in which—contrary to the common treatment of metal ions in such simulations—the position or even coordination of the ion does not have to be constrained using preexisting knowledge. It has been demonstrated that the produced models are capable of reproducing key properties of relevant Pt(II) complexes but that the POSSIM formalism yields more accurate values for energies of formation than the OPLS-AA model. This Pt(II) model was employed—along with previously developed Cu(I) parameters—to investigate the binding of platinum to the protein Atox1, a human copper chaperone implicated in the resistance mechanism of cisplatin and other platinum antitumor compounds. In collaboration with the Dmitriev and Bernholc groups, we used our models to inform and refine spectroscopic experiments as well as to serve as starting points for high-performance quantum calculations. It was shown that under physiological redox conditions, copper(I) and cisplatin can form large polymers with glutathione. These polymers were capable of transferring copper(I) to apo-Atox1 or to platinum(II) to copper-loaded Atox1. Analysis of the simultaneous binding of copper(I) and platinum(II) to Atox1 was found to occur through the formation of copper–sulfur–platinum bridges, where copper is coordinated by three sulfur atoms and platinum by four sulfur atoms. With the goal of using a simple model to be able to quickly estimate the acid disassociation constants of proteins, PKA17 has been developed and tested. PKA17 is a coarse-grain grid-based method and software tool for accurately and rapidly calculating protein pKa values given an input PDB structure file. During development, parameter fitting was carried out using a compilation of 442 Asp, Glu, His, and Lys residues that had both high-resolution PDB structures and published experimental pKa values available. Applying our PKA17 model, the calculated average unsigned error and RMSD for the residue set were found to be 0.628 and 0.831 pH units, respectively. As a benchmark for comparison, the same residue set was evaluated with the PROPKA software package which resulted in an average unsigned error of 0.761 pH units and an RMSD of 1.063 pH units. Finally, a web interface for the PKA17 software was developed and deployed (http://users.wpi.edu/~jpcvitkovic/pka_calc.html) to make PKA17 available to the wider scientific community.

Nesta tese, um estudo é feito do modelo bi-dimensional descrito pela densidade de Lagrangeana. Na primeira parte deste trabalho, discute- se a teoria de perturbação na constante de acoplamento g para as funções de Green. Mostra-se como e possível construir um esquema de renormalização de modo que não sejam induzidas interações quadri-lineares nos férmions quando M=0. Aplicando a identidade de Ward da corrente axial, prova-se então, que o limite M = 0 coincide, em qualquer ordem de g, com as funções de Green do modelo com massa do fermion nula, que e exatamente solúvel. Na segunda parte da tese , o termo de massa do férmion em L é tratado como uma perturbação em torno da teoria não livre. Após uma resomação parcial da série perturbativa, mostra-se que as funções de Green Euclidianas tornam-se finitas no intervalo O g POT. 2< pela introdução de um contra-termo proporcional a (:cos2g:1). A quebra da invariança pelas transformações - POT. 5 é verificada explicitamente por meio da identidade de Ward da corrente axial. / In this thesis, a study is made of the two-dimensional model described by the Lagrangean density. In the first part of this work, the perturbation theory in the coupling constant g is discussed for the Green functions. It is shown how to construct a renormalization scheme such that no four-linear interactions in the fermion field are induceded when m=0 by applying the axial current Ward identity, it is then proved that the M=O limit agrees, in every order of g, with the Green functions of the soluble model with massless fermion. In the second part of the thesis, the fermion mass term in L is considered as a perturbation on the interacting theory. After a partial resummation of the perturbative series, it is shown that the Euclidean Green functions are made finite for 0g²< introducing a counter-term proportional to (:cos2g:1). Breaking of -5 symmetry is explicity verified through the axial current Ward identity.

A confiabilidade do produto é um dos principais atributos da sua qualidade, porém a melhoria contínua desta confiabilidade é um objetivo inalcançável para as empresas, principalmente após o processo de globalização, no qual as empresas locais não têm como competidores apenas as empresas regionais ou nacionais, mas também as outras empresas mundiais. Outro fator importante, para o estabelecimento da confiabilidade, é o cliente que têm aumentado as suas exigências num processo contínuo, em que os aspectos de conformidade às especificações do projeto estão se tornando critério de compra. Este trabalho, através de um estudo de caso, apresenta a análise de um processo de atendimento a itens não conformes e propõe melhorias neste processo, visando agilizar a solução de problemas de campo. Para isso será avaliada a confiabilidade da empresa, desde a comunicação do cliente, passando pelo revendedor e da própria empresa, até a metodologia utilizada para a análise das falhas de campo dos produtos existentes. Os registros e informações da área de suporte e serviços, serão fundamentais para a introdução de melhorias para o procedimento atualmente em uso pela empresa. / The reliability of a product is one of the main attributes of its quality, however continuous improvement of its reliability is a never-ending journey for companies, especially those with global processes, as they must complete with other regional, national and global companies. Another important factor in determining the reliability of a product is the understanding of the critical customer requirements. Due to market globalization, consumers now have access to a greater variety of products and are better able to make comparisons between similar items. This ability drives consumers to constantly change or refine their critical requirements that ultimately influence their purchasing decisions. This case study presents an analysis of a process for monitoring product non-conformances and proposes process improvements aimed at speeding up the solution to field problems. To do this, company reliability will be analyzed in terms of the path of communication of product problems from the customer to the dealer, the dealer to the factory and from the factory to the methodology used to analyze field failures. Information from the product support and services area will be fundamental to the introduction of improvements to the current field failure processes.

by Leung Tak. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 76-77). / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Elliptic curve --- p.4 / Chapter 2.1 --- Elliptic Curve in Normal Form --- p.4 / Chapter 2.2 --- Geometry and Group Law --- p.7 / Chapter 2.3 --- Special Class of Elliptic Curves --- p.10 / Chapter 2.4 --- Mordell's Conjecture --- p.12 / Chapter 2.5 --- Torsion Group --- p.14 / Chapter 2.6 --- Selmer Group and Tate-Shafarevitch. Group --- p.16 / Chapter 2.7 --- Endomorphism of Elliptic Curves --- p.19 / Chapter 2.8 --- Formal Group over Elliptic Curves --- p.23 / Chapter 2.9 --- The Finite Field Case --- p.26 / Chapter 2.10 --- The Local Field Case --- p.27 / Chapter 2.11 --- The Global Field Case --- p.29 / Chapter 3 --- Class Field Theory --- p.31 / Chapter 3.1 --- Valuation and Local Field --- p.31 / Chapter 3.2 --- Unramified and Totally Ramified Extensions and Their Norm Groups --- p.35 / Chapter 3.3 --- Formal Group and Abelian Extension of Local Field --- p.36 / Chapter 3.4 --- Abelian Extenion and Norm Residue Map --- p.41 / Chapter 3.5 --- Finite Extension and Ramification Group --- p.43 / Chapter 3.6 --- "Hilbert Symbols [α, β］w and (α, β)f" --- p.46 / Chapter 3.7 --- Adele and Idele --- p.48 / Chapter 3.8 --- Galois Extension and Kummer Extension --- p.50 / Chapter 3.9 --- Global Reciprocity Law and Global Class Field --- p.52 / Chapter 3.10 --- Ideal-Theoretic Formulation of Class Field Theory --- p.57 / Chapter 4 --- Hasse-Weil L-function of elliptic curves --- p.60 / Chapter 4.1 --- Classical Zeta Functions and L-functions --- p.60 / Chapter 4.2 --- Congruence Zeta Function --- p.63 / Chapter 4.3 --- Hasse-Weil L-function and Birch-Swinnerton-Dyer Conjecture --- p.64 / Chapter 4.4 --- A Sketch of the Proof from the Joint Paper of Coates and Wiles --- p.67 / Chapter 4.5 --- The works of other mathematicians --- p.73