In this thesis, we mainly study the structure of $D_9$-brane Chan-Paton factors in Type II orientifold $O_p^{\pm}$ theories. An explicit structure is found through a thorough and systematic derivation. For this purpose, we give a complete analysis of the worldsheet parity square action for all p-q open strings (i.e, the strings starting from $D_p$-branes and ending on $D_q$-branes), which is an extension of Gimon-Polchinski's work on the parity square action for p-q strings with $p-q$ even. We also formulate the rules for computing the scattering amplitudes of open strings ending on D-branes. These are important to build phenomenological models in string theory. As an application to the mathematical aspects of string theory, we confirm the proposal that the D-brane charges in Type II orientifolds are classified by the KR-theory groups. All these results will appear in our paper\footnote{Dongfeng Gao and Kentaro Hori, Clifford Algebras and Chan-Paton Factors, to appear.}. We also show some preliminary results on the B-type D-branes in the orientifolds of linear sigma models. A typical linear sigma model has both a geometric phase and a Landau-Ginzberg phase over its K\"ahler moduli space. The B-type D-branes are described by suitable categories in a linear sigma model and its phases. The orientifold projection induces parity mappings on the various categories. By looking at the transportation of invariant branes in the moduli space, we find the relations among the parity mappings of different phases in the quintic model.

In this thesis, we mainly study the structure of $D_9$-brane Chan-Paton factors in Type II orientifold $O_p^{\pm}$ theories. An explicit structure is found through a thorough and systematic derivation. For this purpose, we give a complete analysis of the worldsheet parity square action for all p-q open strings (i.e, the strings starting from $D_p$-branes and ending on $D_q$-branes), which is an extension of Gimon-Polchinski's work on the parity square action for p-q strings with $p-q$ even. We also formulate the rules for computing the scattering amplitudes of open strings ending on D-branes. These are important to build phenomenological models in string theory. As an application to the mathematical aspects of string theory, we confirm the proposal that the D-brane charges in Type II orientifolds are classified by the KR-theory groups. All these results will appear in our paper\footnote{Dongfeng Gao and Kentaro Hori, Clifford Algebras and Chan-Paton Factors, to appear.}. We also show some preliminary results on the B-type D-branes in the orientifolds of linear sigma models. A typical linear sigma model has both a geometric phase and a Landau-Ginzberg phase over its K\"ahler moduli space. The B-type D-branes are described by suitable categories in a linear sigma model and its phases. The orientifold projection induces parity mappings on the various categories. By looking at the transportation of invariant branes in the moduli space, we find the relations among the parity mappings of different phases in the quintic model.

The main goal of string phenomenology is to find a convincing connection be- tween realistic particle physics and string theory. An extended object called D-brane in string theory is shown as a very powerful tool to resolve phenomenology problems. D-branes, D standing for Dirichlet boundary conditions, naturally appear in the T- dual space along one of the toroidally compactified dimensions in non-perturbative Type I theory. A D-brane forms an U(1) gauge group and the group structure can be enriched by Chan-Paton indices with multiple coincided D-branes and orientifold ac- tions. Oribfolds define fixed points of the compactified space and break the theory to N = 1 supersymmetry, and the extended orientifold from world-sheet parity projects the brane image to help cancel the anomalies. Strings at the intersections of two D-branes (Type IIA) form massless chiral fermions as bi-fundamental representations of the gauge groups of the intersecting branes. With these properties, we construct Grand Unification Theory (GUT) and standard-like models by intersecting D-brane configuration on T6/(Z2 × Z2) orientifold. Also, supergravity and geometrical fluxes are introduced to stabilize the moduli. In this dissertation, first a brief review of the D-brane theory is discussed, then the complete construction of D-brane configuration on T6/(Z2 × Z2) is presented, and finally some realistic Trinification, Pati-Salam, SU(5) and flipped SU(5) models are constructed and discussed. We present the models both in D-brane wrapping numbers and the corresponding particle spectra.

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University, Diss., 2001--München.

Made available in DSpace on 2014-06-11T19:25:29Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-07-08Bitstream added on 2014-06-13T18:07:03Z : No. of bitstreams: 1 ruedachumbes_ae_me_guara.pdf: 557923 bytes, checksum: 145698e3e42e6e9b8c231fbc61751937 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Nesta dissertação analisamos modelos não-lineares envolvendo campos escalares em d + 1 dimensões do espaço-tempo. Damos ênfase `a questão da estabilidade das soluções clássicas de alguns modelos não-lineares que envolvem interação de dois campos escalares em 1 + 1 dimensões , onde mostramos nossa discordância com os argumentos de estabilidade desenvolvidos por Boya e Casahorran, e Bazeia et al., particularmente no que diz respeito ao desacoplamento das equações para as flutuações dos campos escalares. Revisamos a proposta de Bazeia et al. para eludir o argumento de Derrick. Observamos que a hamiltoniana de estabilidade expressa em d dimensões espaciais não pode ser fatorada como o produto de dois operadores adjuntos um do outro, portanto não podemos garantir que o operador hamiltoniano seja positivo definido. Por último construímos modelos efetivos de um campo escalar acoplado `a gravidade em (4,1) dimensões do espaço. Estes modelos efetivos podem ser aplicados para o caso de cenários cosmológicos, onde o universo é tratado como imerso em uma parede de domínio em uma dimensão extra. O estudo das soluções destes modelos possui uma grande importância para a construção de cenários cosmologicos e melhor entendimento de nosso universo, como por exemplo a formação de branas espessas e a separação de branas. / In this dissertation we analyze nonlinear models involving scalars fields in d+1 spacetime dimensions. We put emphasis on the question of the stability of classical solutions of some models, where we show our disagreement with the arguments of stability developed by Boya and Casahorran and Bazeia et al.; particularly on the decoupling of the differential equations for the fluctuations of the scalars fields. We review the proposal of Bazeia et al. to circumvent the Derrick argument. In our analysis we observe that the Hamiltonian associated to the stability of the systems in d space dimensions can not be factorized as the product of two operators which are adjoint of each other, therefore the positiveness of the Hamiltonian operator is not guaranteed. Finally we build effective models with a scalar field coupled to gravity in (4.1) dimensions of the space-time. Those models, the effective model can be applied to cosmological scenarios, where our universe is taken as imbeded in a domain wall in an extra dimension. The study of the solutions of those models has a great importance for the construction of cosmological scenarios and for the better understanding of our universe, for example, the formation of thick branes and the separation of branes.

Superstring theory is one current, promising attempt at unifying gravity with the other three known forces: the electromagnetic force, and the weak and strong nuclear forces. Though this is still a work in progress, much effort has been put forth toward this goal. A set of specific tools which are used are gauge/gravity dualities. This thesis consists of a specific implementation of gauge/gravity dualities to describe k-strings of strongly coupled gauge theories as objects dual to Dpbranes embedded in confining supergravity backgrounds from low energy superstring field theory. Along with superstring theory, k-strings are also commonly investigated with lattice gauge theory and Hamiltonian methods. A k$string is a colorless combination of quark-anti-quark source pairs, between which a color flux tube develops. The two most notable terms of the k-string energy are, for large quark anti-quark separation L, the tension term, proportional to L, and the Coulombic 1/L correction, known as the Luscher term. This thesis provides an overview of superstring theories and how gauge/gravity dualities emerge from them. It shows in detail how these dualities can be used for the specific problem of calculating the k-string energy in 2+1 and 3+1 space-time dimensions as the energy of Dp-branes in the dual gravitational theory. A detailed review of k-string tension calculations is given where good agreement is found with lattice gauge theory and Hamiltonian methods. In reviewing the k-string tension, we also touch on how different representations of k-strings can be described with Dp-branes through gauge/gravity dualities. The main result of this thesis is how the Luscher term is found to emerge from the energy calculation of Dp-branes. In 2+1 space-time dimensions, we have Luscher term data to compare with from lattice gauge theory, where we find good agreement.

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This dissertation covers two different but related topics: the construction of consistent models in type IIB and heterotic string theories, and the higher derivative couplings for D-brane action, which will enable us to relate some models of type IIB to the heterotic side through duality chain. In the first part, we describe an alternative to the KKLT scenario, in which one can achieve de-Sitter space after fixing all moduli. We fix complex structure moduli and the axio-dilaton by deriving the stability conditions for the critical points of the no-scale scalar potential that governs the dynamics of the complex structure moduli and the axio-dilaton in compactifications of type IIB string theory on Calabi-Yau three-folds. In the second part, we show the existence of a class of flux backgrounds in heterotic string theory. The background metric we will consider is a T2 fibration over a K3 base times four-dimensional Minkowski space. Unbroken space-time supersymmetry determines all background fields except one scalar function which is related to the dilaton. The heterotic Bianchi identity gives the same differential equation for the dilaton, and we will discuss in detail the solvability of this equation for backgrounds preserving an N=2 supersymmetry. In the third part, we obtain the higher derivative D-brane action by using both linearized T-duality and string disc amplitude computation. We evaluate disc amplitude of one R-R field C^(p-3) and two NS-NS fields in the presence of a single Dp-brane in type II string theory. We obtain the action for the higher derivative brane interactions among one R-R field C^(p-3) and two NS-NS B-fields after carefully comparing the supergravity amplitudes with the corresponding string amplitude up to alpha^r2 order. We also show that these higher derivative brane couplings are invariant under both R-R and NS-NS B-field gauge transformations, and compatible with linear T-duality.