The purpose of this thesis is to study a symmetry of string theory known as T-duality. We focus on a particular example establishing the equivalence between a quantized string moving in a circular space of radius R and a dual string moving in a similar space of radius 1/R . We will show that this duality implies that the momentum of the string in one picture becomes the number of times the string is wound around the circle in the dual picture. We present two proofs of T-duality. The first reflects the standard interpretation of T-duality as an isomorphism of quantum theories. The second approach is based on Hull's Double Field Theory.

Orientador: Horatiu Nastase / Resumo: Nesta tese, discutimos três modelos cosmológicos que são baseados direta ou indiretamente em ideias advindas de teoria das cordas. Depois de uma revisão geral de cosmologia em teoria das cordas, um resumo de cosmologia e teoria das cordas é apresentado, com ênfase nos conceitos fundamentais e teóricos. Então descrevemos como o acoplamento camaleônico pode potencialmente afetar as predições de inflação cósmica com campo único, com tratamento cuidadoso dos modos de perturbação cosmológica adiabáticos e de entropia. Além disso uma nova abordagem para a dualidade-T em soluções cosmológicas de supergravidade bosônica é discutida no contexto de teoria dupla de campos. Por fim, propomos uma nova prescrição para o mapa holográfico em cosmologia que pode ser usado para conectar modelos fundamentais de cosmologia holográfica com outras abordagens fenomenológicas. / Doutor

This thesis is devoted to various questions connected with duality. It is composed of two parts.The first part discusses some aspects of timelike T-duality. We explore the possibility of compactification of supergravity theories with various signatures(low energy limit of M-theories which are dual under timelike T-dualities) on parallelizable internal seven dimensional (pseudo-)spheres. We show that, beside the standard theory, only one of the dual theories known as M'-theory can admit such a solution. The effective four dimensional theory is non-supersymmetric and due to the presence of torsion the symmetry of seven dimensional (pseudo-)sphere breaks down to Spin(3, 4). In the second part, in an attempt to have a systematic discussion of gaugings in supergravity, we show the isomorphism between the space of local deformations of the appropriate zero coupling limit of the embedding tensor Lagrangian and that of the second-order scalar-vector Lagrangian, describing the bosonic sector of supergravity ignoring gravity, in a chosen duality frame determined by embedding tensors. We analyze the BV-BRST deformation of a class of scalar-vector coupled Lagrangians, which contains supergravity Lagrangians as examples, and find a set of constraints that guarantee the consistency of the deformations of the Lagrangians. We show in principle that for a large class of theories considered in this thesis, the only deformations are those of the Yang-Mills type associated with a subgroup of the rigid symmetries. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

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In the present project we study compactifications of type IIA/IIB string theories on toroidal orbifolds. We present the moduli space for N=1 four-dimensional reductions and its topological properties. To fix the value of all moduli, we will construct the most general holomorphic superpotential W using a set of T-dual iterations for the fluxes. Using a 3-torus toy-model, we will give an introductory description to the background of these generalised fluxes.

Non-linear sigma models with extended supersymmetry have constrained target space geometries, and can serve as effective tools for investigating and constructing new geometries. Analyzing the geometrical and topological properties of sigma models is necessary to understand the underlying structures of string theory. The most general two-dimensional sigma model with manifest N=(2,2) supersymmetry can be parametrized by chiral, twisted chiral and semichiral superfields. In the research presented in this thesis, N=(4,4) (twisted) supersymmetry is constructed for a semichiral sigma model. It is found that the model can only have additional supersymmetry off-shell if the target space has a dimension larger than four. For four-dimensional target manifolds, supersymmetry can be introduced on-shell, leading to a hyperkähler manifold, or pseudo-supersymmetry can be imposed off-shell, implying a target space which is neutral hyperkähler. Different sigma models and corresponding geometries can be related to each other by T-duality, obtained by gauging isometries of the Lagrangian. The semichiral vector multiplet and the large vector multiplet are needed for gauging isometries mixing semichiral superfields, and chiral and twisted chiral superfields, respectively. We find transformations that close off-shell to a N=(4,4) supersymmetry on the field strengths and gauge potentials of the semichiral vector multiplet, and show that this is not possible for the large vector multiplet. A sigma model parametrized by chiral and twisted chiral superfields can be related to a semichiral sigma model by T-duality. The N=(4,4) supersymmetry transformations of the former model are linear and close off-shell, whereas those of the latter are non-linear and close only on-shell. We show that this discrepancy can be understood from T-duality, and find the origin of the non-linear terms in the transformations.

<p>This thesis considers two different aspects of string theory, the tensionless limit of the string and supersymmetric sigma models with extended supersymmetry. First, the tensionless limit is used to find a IIB supergravity background generated by a tensionless string. The background has the characteristics of a gravitational shock-wave. Then, the quantization of the tensionless string in a pp-wave background is performed and the result is found to agree with what is obtained by taking a tensionless limit directly in the quantized theory of the tensile string. Hence, in the pp-wave background the tensionless limit commutes with quantization. Next, supersymmetric sigma models and the relation between extended world-sheet supersymmetry and target space geometry is studied. The sigma model with N=(2,2) extended supersymmetry is considered and the requirement on the target space to have a bi-Hermitean geometry is reviewed. The Hamiltonian formulation of the model is constructed and the target space is shown to have generalized Kähler geometry. The equivalence between bi-Hermitean geometry and generalized Kähler follows, in this context, from the equivalence between the Lagrangian- and Hamiltonian formulation of the sigma model. Then, T-duality in the Hamiltonian formulation of the sigma model is studied and the explicit T-duality transformation is constructed. It is shown that the transformation is a symplectomorphism, i.e. a generalization of a canonical transformation. Under certain assumptions, the amount of extended supersymmetry present in the sigma model is shown to be preserved under the T-duality transformation. Next, extended supersymmetry in a first order formulation of the sigma model is studied. By requiring N=(2,2) extended world-sheet supersymmetry an intriguing geometrical structure arises and in a special case generalized complex geometry is found to be contained in the new framework.</p>

This thesis considers two different aspects of string theory, the tensionless limit of the string and supersymmetric sigma models with extended supersymmetry. First, the tensionless limit is used to find a IIB supergravity background generated by a tensionless string. The background has the characteristics of a gravitational shock-wave. Then, the quantization of the tensionless string in a pp-wave background is performed and the result is found to agree with what is obtained by taking a tensionless limit directly in the quantized theory of the tensile string. Hence, in the pp-wave background the tensionless limit commutes with quantization. Next, supersymmetric sigma models and the relation between extended world-sheet supersymmetry and target space geometry is studied. The sigma model with N=(2,2) extended supersymmetry is considered and the requirement on the target space to have a bi-Hermitean geometry is reviewed. The Hamiltonian formulation of the model is constructed and the target space is shown to have generalized Kähler geometry. The equivalence between bi-Hermitean geometry and generalized Kähler follows, in this context, from the equivalence between the Lagrangian- and Hamiltonian formulation of the sigma model. Then, T-duality in the Hamiltonian formulation of the sigma model is studied and the explicit T-duality transformation is constructed. It is shown that the transformation is a symplectomorphism, i.e. a generalization of a canonical transformation. Under certain assumptions, the amount of extended supersymmetry present in the sigma model is shown to be preserved under the T-duality transformation. Next, extended supersymmetry in a first order formulation of the sigma model is studied. By requiring N=(2,2) extended world-sheet supersymmetry an intriguing geometrical structure arises and in a special case generalized complex geometry is found to be contained in the new framework.

No description available.

Στην παρούσα διδακτορική διατριβή μελετάμε εφαρμογές οι οποίες σχετίζονται με την μη-Αβελιανή Τ-δυϊκότητα και την αντιστοιχία AdS/CFT. Στο πρώτο μέρος, το οποίο αντιστοιχεί στο πρώτο κεφάλαιο της διατριβής, παρουσιάζουμε συνοπτικά τα απαραίτητα μαθηματικά εργαλεία που απαιτούνται για την καλύτερη κατανόηση των κεφαλαίων που ακολουθούν. Στο δεύτερο μέρος, το οποίο αποτελείται από τα κεφάλαια 2,3 και 4, ασχολούμαστε με την έννοια της μη-Αβελιανής Τ-δυϊκότητας. Ποιο συγκεκριμένα, στο δεύτερο κεφάλαιο παρουσιάζουμε τους κανόνες Buscher της Αβελιανής Τ-δυϊκότητα καθώς και την γενίκευση τους στην μη-Αβελιανή περίπτωση. Επίσης στο κεφάλαιο αυτό δείχνουμε τον τρόπο με τον οποίο μπορούμε να εφαρμόσουμε τους κανόνες της μη-Αβελιανής Τ-δυϊκότητας σε υπόβαθρα υπερβαρύτητας τύπου II τα οποία περιλαμβάνουν πεδία Ramond-Ramond. Η διαδικασία αυτή μπορεί να θεωρηθεί σαν μια τεχνική κατασκευής νέων λύσεων υπερβαρύτητας. Στο τρίτο κεφάλαιο θεωρούμε μια γενική κατηγορία υποβάθρων υπερβαρύτητας με ισομετρία SO(4) στα οποία εφαρμόζουμε τον μετασχηματισμό της μη-Αβελιανής Τ-δυϊκότητας ως προς την υποομάδα SU(2) της ομάδας ισομετρίας. Πραγματοποιώντας διαστατική ελάττωση στην αρχική και την δυϊκή θεωρία καταλήγουμε στην ίδια επταδιάστατη θεωρία. Ως αποτέλεσμα, οποιαδήποτε λύση αυτής της επταδιάστατης θεωρίας μπορεί να ανυψωθεί ταυτόχρονα στο αρχικό και στο δυϊκό υπόβαθρο. Η παρατήρηση αυτή μας παρέχει μια αντιστρεπτή απεικόνιση μεταξύ δυο λύσεων υπερβαρύτητας τύπου II οι οποίες συνδέονται με έναν μετασχηματισμό μη-Αβελιανής Τ-δυϊκότητας. Επίσης, για την συγκεκριμένη περίπτωση υποβάθρων αποδεικνύουμε ότι το δυϊκό υπόβαθρο διατηρεί τη μισή υπερσυμμετρία σε σχέση με το αρχικό. Στο τέταρτο κεφάλαιο μελετάμε τη δράση της μη-Αβελιανής Τ-δυϊκότητας σε μια σειρά από υπόβαθρα με υπερσυμμετρία N=1 των οποίων οι δυϊκές θεωρίες πεδίου είναι γνωστές. Σκοπός του κεφαλαίου αυτού είναι η μελέτη της μη-Αβελιανής Τ-δυϊκότητας στα πλαίσια της αντιστοιχίας AdS/CFT. Αυτό το επιτυγχάνουμε μελετώντας διάφορες ποσότητες των θεωριών πεδίου που αντιστοιχούν στο αρχικό και στο δυϊκό υπόβαθρο. Τέλος, στο πέμπτο κεφάλαιο κάνουμε χρήση τεχνικών ολογραφίας προκειμένου να μελετήσουμε το φαινόμενο της εισαγωγής φερμιονικών προσμίξεων σε τρισδιάστατες θεωρίες ύλης τύπου Chern-Simons, οι οποίες περιλαμβάνουν μεγάλο αριθμό γεύσεων. / In this thesis, we study applications which are related to the non-Abelian T-duality and the AdS/CFT correspondence. In the first part, which corresponds to the first chapter of the present thesis, we briefly present the basic mathematical tools required for the better understanding of the material included in the next chapters. In the second part, which consists of the chapters 2,3 and 4, we deal with the concept of non-Abelian T-duality. More concretely, in the second chapter we present the Buscher rules of the Abelian T-duality and we generalize them to the non-Abelian case. We also show how to implement the rules of non-Abelian T-duality in backgrounds of type II supergravity with non-vanishing Ramond-Ramond fields. This proccess can be seen as a generating technique of new supergravity backgrounds. In the third chapter we consider a general class of supergravity backgrounds with SO(4) isometry and we perform the non-Abelian T-duality transforation with respect to the SU(2) subgroup of SO(4). After a consistent truncation to seven dimensions of both the original and the dual background we reproduce the same seven dimensional theory. As a result, any solution of this seven dimensional theory can be uplifted simultaneously to both the original and the dual background. This provides an invertible map between two solutions of type II supergravity which are related with a non-Abelian T-duality transformation. Also, in the case of supergravity backgrounds considered here, we show that the dual background preserves the half supersymmetry with respect to the original one. In chapter 4, we study the action of non-Abelian T-duality on a series of N=1 supersymmetric backgrounds whose field theory duals are well understood. The aim of this chapter is to study the transformation of non-Abelian T-duality within the framework of the AdS/CFT correspondence. This is done by considering several observables of the field theories that correspond to both the original and the dual backgrounds. Finally, in chapter 5 we use holographic techniques in order to study the effect of the addition of fermionic impurities to the three dimensional Chern-Simons matter theories with a large number of flavors.