Orientador: Nathan Jacob Berkovits / Banca: Horatiu Nastase / Banca: Andrei Mikhailov / Banca: Victor de Oliveira Rivelles / Banca: Vladimir Perchin / Resumo: Esta tese é baseada em parte do meu trabalho de doutoramento e tem como objetivo apresentar uma análise detalhada de algumas propriedades recém abordadas do fantasma b composto no formalismo de espinores puros. Primeiramente será feita uma revisão dos formalismos mínimo e não-mínimo. Em seguida, será apresentada a construção do fantasma b passo a passo, inlcuindo correções quânticas. Por fim, serão estudadas em detalhes suas propriedades fundamentais, ue vão desde a nilpotência até a definição de um possível conjugado, o fantasma c / Abstract: This thesis is based in part of my work during the Ph.D. and aims to present a detailed analysis of some newly studied properties of the composite non-minimal pure spinor b ghost. First, a review of the minimal and non-minimal pure spinor formalisms will be presented. Then, the construction of the non-minimal b ghost will be done step-by-step, including quantum corrections. Finally, some of its fundamental properties will be studied i detail, ranging from nilpotency until the definition of a possible canonical conjugate, the c ghost / Doutor

No description available.

No description available.

No description available.

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. 27 January 2016. / The direct and inverse spectral problems for an inhomogeneous string with an interval of zero density and a concentrated mass at the end point moving with damping are investigated. The partial differential equation is mapped into an ordinary differential equation using separation of variables which in turn is transformed into a Sturm-Liouville differential equation with boundary conditions depending on these parathion variable. The Marchenko approach is employed in the inverse problem to recover the potential, density and other parameters from the knowledge of the two spectra and length of the string.

In this thesis we explore certain limits of the AdS/CFT correspondence for integrability. This is done by calculating the action of the dilatation operator on operators known as restricted Schur polynomials, which are AdS/CFT dual to D3-branes known as giant gravitons. We focus on operators in N = 4 super-Yang-Mills theory, which is dual to type IIB string theory on an AdS5×S5 background. We find that, in various cases, this theory is integrable in a large N non-planar limit.

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, 30.09.2014. / ABSTRACT In this dissertation we study the action of the one loop dilatation operator on operators with a classical dimension of order N. We consider the su(3) and su(2) sectors. The operators in the su(3) sector are constructed using three complex fields X, Y and Z, while operators in the su(2) sector are constructed from only the two complex fields Y and Z. For the operators in these sectors non-planar diagrams contribute already at the leading order in N and the planar and large N limits are distinct. Although the spectrum of anomalous dimensions in su(3) has been computed for this class of operators, previous studies have neglected certain terms which were argued to be small. After dropping these terms diagonalizing the dilatation operator reduces to diagonalizing a set of decoupled oscillators. In this dissertation we explicitly compute the terms which were neglected previously and show that diagonalizing the dilatation operator still reduces to diagonalizing a set of decoupled oscillators. In the su(2) sector the action of the one loop and the two loop dilatation operator reduces to a set of decoupled oscillators and factorizes into an action on the Z fields and an action on the Y fields. Direct computation has shown that the action on the Y fields is the same at one and two loops. In this dissertation, using the su(2) symmetry algebra as well as structural features of field theory, we give compelling evidence that the factor in the dilatation operator that acts on the Y s is given by the one loop expression, at any loop order. I hereby declare that the content of this dissertation is based on my following original works: • R. de Mello Koch, S. Graham and W. Mabanga, “Subleading corrections to the Double Coset Ansatz preserve integrability” (2013) [arXiv:1312.6230v1 [hep-th]] • R. de Mello Koch, S. Graham and I. Messamah, “Higher Loop Nonplanar Anomalous Dimensions from Symmetry” (2013) [arXiv:1312.6227v1 [hep-th]].

Thesis (Ph. D.)--University of Chicago, Dept. of Physics, June 1999. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 150-160). Available also in a digital version from Dissertation Abstracts.

Orientifolds of type II string theory offer a promising toolkit for model builders, especially when one includes not only the usual fluxes from NSNS and RR field strengths, but also fluxes that are T-dual to the NSNS three-form flux. These additional ingredients can help stabilize moduli and lead to D-term contributions to the effective scalar potential. We describe in general how these fluxes appear as parameters of an effective N = 1 supergravity theory in four dimensions for type IIA and type IIB string theory. We also show how these fluxes arise from compactifications on six-dimensional spaces that can be described by toroidal fibers twisted over a toroidal base. This approach leads us to a more subtle treatment of the quantization of the general NSNS fluxes. We illustrate these phenomena with examples of certain orientifolds of T⁶/Z₄. / text