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.

University, Diss., 2001--München.

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.

Cette thèse intitulée « Studies of fractional D-branes in the gauge/gravity correspondence & Flavored Chern-Simons quivers for M2-branes » se place dans le cadre de la théorie des cordes, en physique théorique. Elle consiste en une introduction suivie de deux parties. Dans l'introduction sont résumés les différents outils de théorie des cordes qui seront utilisés. La première partie étudie des théories de type quiver en 3+1 dimensions et leur dual gravitationnel, qui découlent de la considération de D-branes fractionnaires vivant sur des espaces possédant des singularités en codimension complexe un. La thèse principale de cette partie est que la solution de supergravité de Bertolini et al. 2001 and Polchinski 2001 pour des branes de type N=2 a une interprétation dans la théorie des champs de type quiver duale comme un groupe de renormalisation de type cascade qui résulte d'un choix particulier sur la branche de Coulomb de la théorie. Cette compréhension nouvelle permet d'étudier des solutions de supergravité plus générales. Elle donne aussi une plus grande compréhension des branes N=2 dans des contextes avec seulement une supersymmétrie N=1. La second partie de la thèse étudie les quivers de type Chern-Simons, récemment apparus dans la littérature, décrivant des théories en dimension 2+1, qui sont conjecturé dual à des solutions de M-théorie. Il est montré que des théories plus générales que des quivers, possédant également des champs dans la représentation fondamentale des groupes de jauges, permettent la description de M2-branes sur des espaces possédant des singularités de dimension complexe deux, du moins du point de vue de la structure complexe, dans le cas où seules 4 supercharges sont préservées. La thèse principale est que la considération des operateurs monopoles diagonaux dans la théorie de champs N=2 supersymmétrique en 2+1 dimensions, plus une relation entre ces opérateurs proposée comme conjecture, permettent de reproduire l'espace des modules d'une M2-brane sur n'importe quelle géométrie torique ayant des singularités en codimension complexe deux.

University, Diss., 2003--Freiburg (Breisgau). / Parallelt.: The method of the nonlocal effective action in higher-dimensional spacetime models.

In this thesis the close relationship between the topological $K$-homology group of the spacetime manifold $X$ of string theory and D-branes in string theory is examined. An element of the $K$-homology group is given by an equivalence class of $K$-cycles $[M,E,\phi]$, where $M$ is a closed spin$^c$ manifold, $E$ is a complex vector bundle over $M$, and $\phi: M\rightarrow X$ is a continuous map. It is proposed that a $K$-cycle $[M,E,\phi]$ represents a D-brane configuration wrapping the subspace $\phi(M)$. As a consequence, the $K$-homology element defined by $[M,E,\phi]$ represents a class of D-brane configurations that have the same physical charge. Furthermore, the $K$-cycle representation of D-branes resembles the modern way of characterizing fundamental strings, in which the strings are represented as two-dimensional surfaces with maps into the spacetime manifold. This classification of D-branes also suggests the possibility of physically interpreting D-branes wrapping singular subspaces of spacetime, enlarging the known types of singularities that string theory can cope with. / Master of Science

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20168号 / 理博第4253号 / 新制||理||1611(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 福間 將文, 教授 川合 光, 教授 畑 浩之 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

This project is an investigation of a cosmological model consisting of a five dimensional AdS-vacuum with a flux. By discharges in the flux, four dimensional bubbles can nucleate in the vacuum and collide with each other while expanding. Our observable universe is considered to be localized on the membrane of such a bubble. The main purpose of the model was to find a possible explanation for dark energy and inflation. We compute the Friedmann equation for an expanding bubble, as well as analytical expressions for the two slow roll parameters ε and η related to slow roll inflation. We also show that there exists a set of parameters of the model where both slow roll parameters are small enough in order for inflation to last for at least 60 Hubble times. However, our model doesn’t survive all consistency checks with today’s observations. We conclude that even if the resulting slow roll parameters look promising, one has to either look harder for a set of ”good” fundamental parameters of the model, or further develop it to have a chance of surviving all consistency checks. / Populärvetenskaplig sammanfattning: Det här projektet undersöker en kosmologisk modell bestående av ett femdimensionellt vakuum med negativ rumtidkrökning. I vakuumet finns ett elektriskt fält, som i högre dimensioner än fyra kallas flux (flöde). Urladdningar i detta flux gör det möjligt för fyrdimensionella bubblor att uppstå i vakuumet. Dessa vakuumbubblor expanderar snabbt och kommer så småningom att kollidera med varandra. Tanken är att vårt fyrdimensionella observerbara universum utgör en del av membranet på en av dessa expanderande vakuumbubblor. De andra vakuumbubblorna kan - om man vill - betraktas som parallella universum. Målet med detta projekt har varit att hitta en möjlig model för kosmisk inflation - epoken i vårt universums ungdom då rummet expanderade enormt snabbt under en väldigt kort tidsperiod. Inflationen i vår modell äger rum när vakuumbubblan för vårt universum kolliderar med andra vakuumbubblor. Vi lyckades visa att den här modellen kan ge upphov till inflation som varar tillräckligt länge för att det ska stämma överens med dagens observationer av vårt observerbara universum. Dock förutspår modellen även andra saker som inte stämmer överens med observationerna. Vår slutsats är att modellen ser lovande ut, men att man antingen behöver undersöka den noggrannare eller utveckla den på något sätt, om den ska ha en chans att stämma överens med universumet vi observerar. / <p>Presentationen skedde över videolänk på grund av Covid-19.</p>