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Aspects of Holographic Renormalization Group Flows on Curved Manifolds Jewel Kumar Ghosh

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Aspects of Holographic Renormalization Group Flows on Curved Manifolds Jewel Kumar Ghosh Aspects of Holographic Renormalization Group Flows on Curved Manifolds Jewel Kumar Ghosh To cite this version: Jewel Kumar Ghosh. Aspects of Holographic Renormalization Group Flows on Curved Manifolds. Physics [physics]. Université Sorbonne Paris Cité, 2019. English. NNT : 2019USPCC071. tel- 02957677 HAL Id: tel-02957677 https://tel.archives-ouvertes.fr/tel-02957677 Submitted on 5 Oct 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Thèse de doctorat de l’Université Sorbonne Paris Cité Préparée à l’Université Paris Diderot Ecole doctorale Sciences de la Terre et de l'Environnement et Physique de l'Univers, Paris, ED 560 APC - AstroParticule et Cosmologie Aspects of Holographic Renormalization Group Flows on Curved Manifolds Par Jewel Kumar Ghosh Thèse de doctorat de Physique Dirigée par Elias KIRITSIS et Francesco NITTI Présentée et soutenue publiquement à Paris le 19 June 2019 Président du jury : Dudas, Emilian, DR-CNRS , CPHT- Ecole Polytechnique. Rapporteurs : Mateos Sole, David Julian, professeur à l' Universitat de Barcelona, Parnachev, Andrei, professeur à l' Trinity College Dublin. Examinateurs : Petrini, Michela, professeur à l’Sorbonne U, Serreau, Julien, MCF à l'Université Paris Diderot, Laboratoire APC. Directeur de thèse : Kiritsis, Elias Directeur de Recherche au CNRS/Laboratoire APC. Co-directeur de thèse : Nitti, Francesco, Maître de Conférences à l'Université Paris Diderot/APC. ii To, Shitali Ghosh- who brought me to the light of world, Samir Kumar Ghosh- who taught me how to walk in the light of world, Chandita Urmi Ghosh- who brought colors to the light of my world. iv Acknowledgments During this thesis, I am indebted to many people for their help and support. It is my great opportunity to acknowledge their support. I will start by thanking my supervisors Elias Kiritsis and Francesco Nitti for giving me the opportunity to work on this very interesting project. My skills flourished both scientifically and personally. I learned many facets of holog- raphy by working on this thesis under their supervision. I thank Francesco also for his kind support regarding administrative procedures which are in- timidating sometimes. I don't want to miss the opportunity to thank Lukas Witlowski, the person who helped me the most during my thesis. It was indeed a pleasure to collab- orate with him. I thank him for helping me in all the places I got stumbled and providing me support when needed. I also express my gratitude to Leandro Silva Pimenta for his friendship and providing me the necessary support. It was indeed a pleasure to share office with him and discussing many things. I want to thank all the members of the jury board for their availability to attend my thesis defense. I also thank them for reading my thesis. I am greatly indebted to my peers and colleagues from APC, from other in- stitutions of Paris and also from other universities in different places across the globe. I express my gratitude to Pierre Auclair, Makarim Bouyahiaoui, Gabriel Moreau, Calum Murray and Theodoros Papanikolaou for helping me many times. Thank you Alessandra Tonazzo and Yannick Giraud-H´eraudfor providing me with instructions. Thanks goes to B´eatriceSilva and Francois Carr´efor assisting in managing my travel to attend conferences. I also thank all the staffs of APC whose works made my stay comfortable. Last but not the least, I am forever grateful to my parents Samir Kumar Ghosh and Shitali Ghosh for their unconditional love and giving me every- thing they have. I also thank Chandita Urmi Ghosh for her love and support in my hard times and also for her loving care. PhD is challenging, I could not accomplish this hard journey without the kind help and support from many people I know and I don't know, thanks everyone. v R´esum´e La correspondance CFT (Anti-De Sitter) (AdS) / Th´eoriedes champs con- formes (CFT), ´egalement connue sous le nom de dualit´eholographique, con- stitue un lien remarquable entre la th´eoriedes cordes (qui inclut la gravit´e)et les th´eoriesde jauge. Elle relie une CFT dans un espace-temps d-dimensionnel `aune th´eoriede la gravit´edans un espace-temps dimension sup´erieur,´egalement appel´ebloc. Ce dernier a une limite dans laquelle r´esidela th´eoriedu champ conforme. Dans cette th`ese,le sujet d'´etudeest la description holographique des flux de groupes de renormalisation (RG) des th´eories(de champ) sur les espaces-temps `asym´etriemaximale. Le cadre th´eoriqueque j'ai utilis´eest la th´eoried'Einstein-scalaire. L'inclusion du champ scalaire dynamique cor- respond `ala rupture de l'invariance conforme aux limites. Dans ce travail, les limites et les tranches du bloc sont choisies pour ^atredes espaces-temps `a sym´etriemaximale et l'´evolution des champs en bloc est ´etudi´ee.Il d´ecritles ´ecoulements RG holographiques sur des vari´et´escourbes. De plus, deux ap- plications sont pr´esent´eesdans cette th`ese.La premi`ereapplication s'inscrit dans le contexte des th´eor`emesF et la seconde concerne un defaut incurv´e dans les flux RG holographiques en masse. Les th´eor`emesF pour les th´eories de champs quantiques (QFT) d´efinies dans des espaces-temps tridimensionnels exigent l'existence de fonctions dites F. Ce sont des fonctions d´ecroissantes de fa¸conmonotone le long du flux RG. Dans ce travail, de nouvelles fonctions F pour les th´eoriesholographiques ont ´et´ed´ecouvertes. Elles sont construites `apartir de l'action sur la paroie d'une solution de flux holographique RG sur une sph`ere`a3-sph`eres. Ils permettent une interpr´etationentropique, fournissant ainsi un lien direct entre la formulation entropique du th´eor`emeF et sa d´efinitionen termes d'´e nergie libre. La deuxi´emeapplication des flux RG holographiques explor´eedans cette th`esese situe dans le contexte de mod`elesaffichant un m´ecanismed'auto- ajustement en tant que r´esolutionpropos´eedu probl´emede la constante cos- mologique (CC). Dans ces mod`eles,notre univers `a4-dimensions est r´ealis´e comme une brane int´egr´eedans un volume `a5-dimensions. Ce cadre per- met des solutions o`ula g´eom´etriede la brane est plate malgr´ela pr´esence d'une ´energiede vide non triviale sur son worldvolume. Ceci est appel´e r´eglageautomatique. De chaque c^ot´ede la brane, les solutions sont des flux RG holographiques. Le nouvel aspect introduit dans cette th`eseconsiste `a utiliser les flux RG holographiques sur des vari´et´escourbes, ce qui permet `ason tour d'´etudierdes solutions `ar´eglageautomatique dans lesquelles la brane est ´egalement courbe. vi Mots-cl´es : Holographie, dualit´eGauge/Gravit´e,AdS/CFT, flux RG, transition de phase, courbure, monde de Barne. vii Abstract The Anti-de Sitter (AdS)/Conformal Field Theory (CFT) correspondence, also known as holographic duality, is a remarkable connection between string theory (which includes gravity) and gauge theories. It relates a CFT in a d- dimensional space-time to a gravity theory in higher dimensional space-time which is also referred to as the bulk. The latter has a boundary on which the conformal field theory may be thought to reside. In this thesis, the subject of study is the holographic description of Renor- malization Group (RG) flows of (field) theories on maximally symmetric space-times. The theoretical framework I used is Einstein-scalar theory. In- clusion of the dynamical scalar field corresponds to breaking boundary con- formal invariance. In this work, both the boundary and bulk slices are chosen to be maximally symmetric space-times and the evolution of bulk fields is studied. It describes holographic RG flows on curved manifolds. Further- more, two applications are presented in this thesis. The first application is in the context of F-theorems and the second is regarding a curved defect in the bulk holographic RG flows. F-theorems for Quantum Field Theories (QFT) defined on 3-dimensional space-times demand the existence of so-called F-functions. These are mono- tonically decreasing functions along the RG flow. In this work, new F- functions for holographic theories have been found which are constructed from the on-shell action of a holographic RG flow solution on a 3-sphere. They allow an entropic interpretation, therefore providing a direct connec- tion between the entropic formulation of the F-theorem and its definition in terms of free energy. The second application of holographic RG flows explored in this thesis is in the context of models displaying a self-tuning mechanism as a proposed resolution of the cosmological constant (CC) problem. In these models, our 4-dimensional universe is realized as a brane embedded in a 5-dimensional bulk. This framework allows solutions where the brane geometry is flat de- spite of the presence of non-trivial vacuum energy on its worldvolume. This is referred to as self-tuning. On each side of the brane, the solutions are holographic RG flows. The new aspect introduced in this thesis is to use the holographic RG flows on curved manifolds, which in turn allows the study of self-tuning solutions where the brane is also curved. Keywords: Holography, Gauge/Gravity duality, AdS/CFT, RG flows, phase transition, curvature, barne-world. viii Contents 1 Introduction 1 1.1 Motivation .
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