| Detailed view | pastel-00002178, version 1 |
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| Defence date | 2006-10-06 |
| Physique, optique | |
| Library | Ecole Polytechnique |
| Keywords | Théories de cordes – Solutions exactes – Déformation marginales |
| : http://www.imprimerie.polytechnique.fr/Theses/Files/Orlando.pdf | |
| English title | String theory : exact solutions, marginal deformations and hyperbolic spaces. |
| English abstract | This thesis is almost entirely devoted to studying string theory backgrounds characterized by simple geometrical and integrability properties. The archetype of this type of system is give! n by Wess-Zumino-Witten models, describing string propagation in a group manifold or, equivalently, a class of conformal field theories with current algebras. We study the moduli space of such models by using truly marginal deformations. Particular emphasis is placed on asymmetric deformations that, together with the cft description, enjoy a very nice spacetime interpretation in terms of the underlying Lie algebra. Then we take a slight detour so to deal with off-shell systems. Using a renormalization-group approach we describe the relaxation towards the symmetrical equilibrium situation. In the final chapter we consider backgrounds with Ramond-Ramond field and in particular we analyze, in the supergravity approxidirect products of constant-curvature spaces and find solutions with hyperbolic spaces. |
| 1 Introduction 1 2 Wess-Zumino-Witten Models 5 Wess-Zumino-Witten models constitute a large class of the exact string theory solutions which we will use as starting points for most of the analysis in the following. In this chapter we see how they can be studied from different perspectives and with different motivations both from a target space and world-sheet point of view. 2.1 The two-dimensional point of view . . . . . . . . . . . . . . . . . 5 2.2 The target space point of view . . . . . . . . . . . . . . . . . . . . 14 3 Deformations 17 In this rather technical chapter we describe marginal deformations of Wess-Zumino-Witten models. The main purpose for these constructions is to reduce the symmetry of the system while keeping the integrability properties intact, trying to preserve as many nice geometric properties as possible. 3.1 Deformed WZW models: various perspectives . . . . . . . . . . . 18 3.2 Background fields for the asymmetric deformation . . . . . . . . 22 3.3 Geometry of squashed groups . . . . . . . . . . . . . . . . . . . . 26 3.4 A no-renormalization theorem . . . . . . . . . . . . . . . . . . . 28 3.5 Partition functions . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.6 The deformation as a gauging . . . . . . . . . . . . . . . . . . . . 36 4 Applications 43 In this chapter we present some of the applications for the construction outlined above. After an analysis of the most simple (compact and noncompact) examples, we describe the near-horizon geometry for the Bertotti- Robinson black hole, show some new compactifications and see how Horne and Horowitz's black string can be described in this framework and generalized via the introduction of an electric field. 4.1 The two-sphere CFT . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2 SL(2,R) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.3 Near horizon geometry for the Bertotti-Robinson black hole . . 60 4.4 The three-dimensional black string revisited . . . . . . . . . . . 62 4.5 New compactifications . . . . . . . . . . . . . . . . . . . . . . . . 76 5 Squashed groups in type II 85 In this chapter we start deviating from the preceding ones because we will no longer deal with WZW models but with configurations in which the group manifold geometry is sustained by RR fields. In particular, then, we see how the squashed geometries can be obtained in type II theories by Tdualizing black brane configurations. 5.1 SL(2,R) × SU(2) as a D-brane solution . . . . . . . . . . . . . . 85 5.2 T duality with RR fields . . . . . . . . . . . . . . . . . . . . . . . . 86 5.3 The squashed sphere . . . . . . . . . . . . . . . . . . . . . . . . . 88 6 Out of the conformal point: Renormalization Group Flows 91 This chapter is devoted to the study of the relaxation of squashed WZW models further deformed by the insertion of non-marginal operators. The calculation is carried from both the target space and world-sheet points of view, once more highlighting the interplay between the two complementary descriptions. In the last part such techniques are used to outline the connection between the time evolution and the RG-flow which is seen as a large friction limit description; we are hence naturally led to a FRW-type cosmological model. 6.1 The target space point of view . . . . . . . . . . . . . . . . . . . . 92 6.2 The CFT approach . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.3 RG flow and friction . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.4 Cosmological interpretation . . . . . . . . . . . . . . . . . . . . . 110 7 Hyperbolic Spaces 115 In this chapter we investigate type II and M-theory geometries written as direct products of constant-curvature spaces. We find in particular a class of backgrounds with hyperbolic components and we study their stability with respect to small fluctuations. 7.1 M-theory solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 115 7.2 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 7.3 Type IIB backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . 128 8 Conclusions and further perspectives 133 A Table of conventions 135 B Explict parametrizations for some Lie groups 137 B.1 The three-sphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 B.2 AdS3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 B.3 SU (3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 B.4 USp (4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 C Symmetric deformations of SL(2,R) 147 D Spectrum of the SL(2,R) super-WZW model 149 Bibliography 153 |
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| pastel-00002178, version 1 | |
| http://pastel.archives-ouvertes.fr/pastel-00002178 | |
| oai:pastel.archives-ouvertes.fr:pastel-00002178 | |
| From: Ecole Polytechnique <> | |
| Submitted on: Thursday, 29 July 2010 11:01:10 | |
| Updated on: Thursday, 29 July 2010 11:02:31 | |




