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Download or read book Aspects of Holographic Renormalization Group Flows on Curved Manifolds written by Jewel Kumar Ghosh and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 eld theory may be thought to reside. In this thesis, the subject of study is the holographic description of Renormalization Group (RG) fows of (field) theories on maximally symmetric space-times. The theoretical framework I used is Einstein-scalar theory. Inclusion of the dynamical scalar field corresponds to breaking boundary conformal 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. Furthermore, 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 monotonically 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 connection 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 despite 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.