The concept of faster than light travel in general relativity is examined, starting with a review of the Alcubierre metric. This spacetime, although incredible in its implications, has certain unavoidable problems which are discussed in detail. It is demonstrated that in order to describe faster than light travel without any ambiguities, a coordinate independent description is much more convenient. An alternative method of describing superluminal travel is then proposed, which has similarities to the Krasnikov tube.

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.

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

We discuss the target space pseudoduality in supersymmetric sigma models on symmetric spaces. We first consider the case where sigma models based on real compact connected Lie groups of the same dimensionality and give examples using three dimensional models on target spaces. We show explicit construction of nonlocal conserved currents on the pseudodual manifold. We then switch the Lie group valued pseudoduality equations to Lie algebra valued ones, which leads to an infinite number of pseudoduality equations. We obtain an infinite number of conserved currents on the tangent bundle of the pseudodual manifold. Since pseudoduality imposes the condition that sigma models pseudodual to each other are based on symmetric spaces with opposite curvatures (i.e. dual symmetric spaces), we investigate pseudoduality transformation on the symmetric space sigma models in the third chapter. We see that there can be mixing of decomposed spaces with each other, which leads to mixings of the following expressions. We obtain the pseudodual conserved currents which are viewed as the orthonormal frame on the pullback bundle of the tangent space of G tilde which is the Lie group on which the pseudodual model based. Hence we obtain the mixing forms of curvature relations and one loop renormalization group beta function by means of these currents. In chapter four, we generalize the classical construction of pseudoduality transformation to supersymmetric case. We perform this both by component expansion method on manifold M and by orthonormal coframe method on manifold SO(M). The component method produces the result that pseudoduality tranformation is not invertible at all points and occurs from all points on one manifold to only one point where riemann normal coordinates valid on the second manifold. Torsion of the sigma model on M must vanish while it is nonvanishing on M tilde, and curvatures of the manifolds must be constant and the same because of anticommuting grassmann numbers. We obtain the similar results with the classical case in orthonormal coframe method. In case of super WZW sigma models pseudoduality equations result in three different pseudoduality conditions; flat space, chiral and antichiral pseudoduality. Finally we study the pseudoduality tansformations on symmetric spaces using two different methods again. These two methods yield similar results to the classical cases with the exception that commuting bracket relations in classical case turns out to be anticommuting ones because of the appearance of grassmann numbers. It is understood that constraint relations in case of non-mixing pseudoduality are the remnants of mixing pseudoduality. Once mixing terms are included in the pseudoduality the constraint relations disappear.

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Résumé anglais: This thesis consists of an introductory text followed by two separate parts which may be read independently of each other. In Part I we analyze certain hyperbolic structures arising when studying gravity in the vicinity of spacelike singularities (the BKL-limit). In this limit, spatial points decouple and the dynamics exhibits ultralocal behaviour which may be mapped to an auxiliary problem given in terms of a (possibly chaotic) hyperbolic billiard. In all supergravities arising as low-energy limits of string theory or M-theory, the billiard dynamics takes place within the fundamental Weyl chambers of certain hyperbolic Kac-Moody algebras, suggesting that these algebras generate hidden infinite-dimensional symmetries of gravity. We investigate the modification of the billiard dynamics when the original gravitational theory is formulated on a compact spatial manifold of arbitrary topology, revealing fascinating mathematical structures known as galleries. We further use the conjectured hyperbolic symmetry E10 to generate and classify certain cosmological (S-brane) solutions in eleven-dimensional supergravity. Finally, we show in detail that eleven-dimensional supergravity and massive type IIA supergravity are dynamically unified within the framework of a geodesic sigma model for a particle moving on the infinite-dimensional coset space E10/K(E10). Part II of the thesis is devoted to a study of how (U-)dualities in string theory provide powerful constraints on perturbative and non-perturbative quantum corrections. These dualities are typically given by certain arithmetic groups G(Z) which are conjectured to be preserved in the effective action. The exact couplings are given by moduli-dependent functions which are manifestly invariant under G(Z), known as automorphic forms. We discuss in detail various methods of constructing automorphic forms, with particular emphasis on a special class of functions known as (non-holomorphic) Eisenstein series. We provide detailed examples for the physically relevant cases of SL(2,Z) and SL(3,Z), for which we construct their respective Eisenstein series and compute their (non-abelian) Fourier expansions. We also discuss the possibility that certain generalized Eisenstein series, which are covariant under the maximal compact subgroup K(G), could play a role in determining the exact effective action for toroidally compactified higher derivative corrections. Finally, we propose that in the case of rigid Calabi-Yau compactifications in type IIA string theory, the exact universal hypermultiplet moduli space exhibits a quantum duality group given by the emph{Picard modular group} SU(2,1;Z[i]). To verify this proposal we construct an SU(2,1;Z[i])-invariant Eisenstein series, and we present preliminary results for its Fourier expansion which reveals the expected contributions from D2-brane and NS5-brane instantons. / Résumé francais: Cette thèse est composée d'une introduction suivie de deux parties qui peuvent être lues indépendemment. Dans la première partie, nous analysons des structures hyperboliques apparaissant dans l'étude de la gravité au voisinage d'une singularité de type espace (la limite BKL). Dans cette limite, les points spatiaux se découplent et la dynamique suit un comportement ultralocal qui peut être reformulé en termes d'un billiard hyperbolique (qui peut être chaotique). Dans toutes les supergravités qui sont des limites de basse énergie de théories de cordes ou de la théorie M, la dynamique du billiard prend place à l'intérieur des chambres de Weyl fondamentales de certaines algèbres de Kac-Moody hyperboliques, ce qui suggère que ces algèbres correspondent à des symétries cachées de dimension infinie de la gravité. Nous examinons comment la dynamique du billard est modifiée quand la théorie de gravité originale est formulée sur une variété spatiale compacte de topologie arbitraire, révélant ainsi de fascinantes structures mathématiques appelées galleries. De plus, dans le cadre de la supergravité à onze dimensions, nous utilisons la symétrie hyperbolique conjecturée E10 pour engendrer et classifier certaines solutions cosmologiques (S-branes). Finalement, nous montrons en détail que la supergravité à onze dimensions et la supergravité de type IIA massive sont dynamiquement unifiées dans le contexte d'un modèle sigma géodesique pour une particule se déplaçant sur l'espace quotient de dimension infinie E10/K(E10). La deuxième partie de cette thèse est consacrée à étudier comment les dualités U en théorie des cordes fournissent des contraintes puissantes sur les corrections quantiques perturbatives et non perturbatives. Ces dualités sont typiquement données par des groupes arithmétiques G(Z) dont il est conjecturé qu'ils préservent l'action effective. Les couplages exacts sont donnés par des fonctions des moduli qui sont manifestement invariantes sous G(Z), et qu'on appelle des formes automorphiques. Nous discutons en détail différentes méthodes de construction de ces formes automorphiques, en insistant particulièrement sur une classe spéciale de fonctions appelées séries d'Eisenstein (non holomorphiques). Nous présentons comme exemples les cas de SL(2,Z) et SL(3,Z), qui sont physiquement pertinents. Nous construisons les séries d'Eisenstein correspondantes et leurs expansions de Fourier (non abéliennes). Nous discutons également la possibilité que certaines séries d'Eisenstein généralisées, qui sont covariantes sous le sous-groupe compact maximal, pourraient jouer un rôle dans la détermination des actions effectives exactes pour les théories incluant des corrections de dérivées supérieures compactifiées sur des tores.

Symphonic Engagement is a longitudinal study spanning six years, investigating the reasons and benefits for, and the impact on twelve urban public school students who decided to use their free time to participate and be engaged in extra-curricular activities in string orchestras. Literature and research inform us that the arts can play a significant role in the curriculum, inside and outside school, and this study discusses: the connection of the music curriculum to students’ future lives after secondary school graduation; the place of music education in the curriculum; music in our society; music and the brain; the effect of after-school programs on student engagement; and the pedagogy of arts education. Case study is the qualitative methodology used in this research. Data comes from interviews, field notes, and questionnaires that explore and interrogate the issues surrounding music education. Twelve young participants, from different gender, ethnic, and socio-economic backgrounds, were interviewed about their lived experiences and involvement with string orchestras, and on the ways in which these experiences have affected them as students and as members of society. The analysis of the data reveals connections between the author’s arts experiences in the public school system, and those of the twelve students interviewed. The teacher-student relationship, equity, family influence, and technology are discussed as factors that can strengthen programs for youth, by deepening engagement in school experiences. This study explores why some teachers and students choose to participate or become engaged in extra-curricular activities and examines the impact on educational communities, on the future direction of string education, and on the relationship of the teaching/learning experience.

Symphonic Engagement is a longitudinal study spanning six years, investigating the reasons and benefits for, and the impact on twelve urban public school students who decided to use their free time to participate and be engaged in extra-curricular activities in string orchestras. Literature and research inform us that the arts can play a significant role in the curriculum, inside and outside school, and this study discusses: the connection of the music curriculum to students’ future lives after secondary school graduation; the place of music education in the curriculum; music in our society; music and the brain; the effect of after-school programs on student engagement; and the pedagogy of arts education. Case study is the qualitative methodology used in this research. Data comes from interviews, field notes, and questionnaires that explore and interrogate the issues surrounding music education. Twelve young participants, from different gender, ethnic, and socio-economic backgrounds, were interviewed about their lived experiences and involvement with string orchestras, and on the ways in which these experiences have affected them as students and as members of society. The analysis of the data reveals connections between the author’s arts experiences in the public school system, and those of the twelve students interviewed. The teacher-student relationship, equity, family influence, and technology are discussed as factors that can strengthen programs for youth, by deepening engagement in school experiences. This study explores why some teachers and students choose to participate or become engaged in extra-curricular activities and examines the impact on educational communities, on the future direction of string education, and on the relationship of the teaching/learning experience.