Finite Cutoff AdS5_{5} Holography and the Generalized Gradient Flow

Recently proposed double trace deformations of large $N$ holographic CFTs in four dimensions define a one parameter family of quantum field theories, which are interpreted in the bulk dual as living on successive finite radius hypersurfaces. The transformation of variables that turns the equation defining the deformation of a four dimensional large $N$ CFT by such operators into the expression for the radial ADM Hamiltonian in the bulk is found. This prescription clarifies the role of various functions of background fields that appear in the flow equation defining the deformed holographic CFT, and also their relationship to the holographic anomaly. The effect of these deformations can also be seen as triggering a generalized gradient flow for the fields of the induced gravity theory obtained from integrating out the fundamental fields of the holographic CFT. The potential for this gradient flow is found to resemble the two derivative effective action previously derived using holographic renormalization.Comment: 15 pages, no figures, references update

Background independent holographic dual to TTˉT\bar{T} deformed CFT with large central charge in 2 dimensions

The geometerization of the renormalization group flow triggered by the $T\bar{T}$ deformation of large $c$ conformal field theories in two dimensions is presented. This entails the construction of the off shell Einstein-Hilbert action in three dimensions from said renormalization group flow. The crucial ingredient to this construction will be the encoding of general covariance in the emergent bulk theory in a very particular form of the Wess--Zumino consistency conditions. The utilisation of the local renormalization group, which requires putting the theory under consideration on an arbitrary background geometry, supplemented by the aforementioned covariance condition ensures that the whole construction is background independent.Comment: 13 pages, no figure

Non-Hodgkin’s Lymphoma of the Uterine Cervix

Non Hodgkin’s Lymphoma (NHL) causes many deaths worldwide and its incidence is increasing. They occur commonly in middle aged and elderly people and are disseminated at diagnosis. We present an interesting case of NHL in a 52 years old female, who presented with past a history of postmenopausal bleeding. A 3 x 5 cms endocervical polyp was noticed in the cervix. Biopsy of the polyp revealed it to be a CD20-positive diffuse large B-cell (DLBCL)-type NHL. She was diagnosed as stage IE after staging work-up. She attained a complete response, and has been in remission for 1 year 8 months

The Canonical Lagrangian Approach To Three-Space General Relativity

We study the action for the three-space formalism of General Relativity, better known as the BF\'O (Barbour--Foster--\'O Murchadha) action, which is a square-root BSW (Baierlein--Sharp--Wheeler) action. In particular, we explore the (pre)symplectic structure by pulling it back via a Legendre map to the tangent bundle of the configuration space of this action. With it we attain the canonical Lagrangian vector field which generates the gauge transformations (3-diffeomorphisms) and the true physical evolution of the system. This vector field encapsulates all the dynamics of the system. We also discuss briefly the observables and perennials for this theory. We then present a symplectic reduction of the constrained phase space.Comment: 12 pages, 4 figures, modified in accordance with reviewers' comments. Accepted for publication in General Relativity and Gravitatio