Spacetime Entanglement with f(R) Gravity

We study the entanglement entropy of a general region in a theory of induced gravity using holographic calculations. In particular we use holographic entanglement entropy prescription of Ryu-Takayanagi in the context of the Randall-Sundrum 2 model while considering general f(R) gravity in the bulk. Showing the leading term is given by the usual Bekenstein-Hawking formula, we confirm the conjecture by Bianchi and Myers for this theory. Moreover, we calculate the first subleading term to entanglement entropy and show they agree with the Wald entropy up to extrinsic curvature terms.Comment: 16 pages, 2 figure

Non-equilibrium steady state in the hydro regime

We study the existence and properties of the non-equilibrium steady state which arises by putting two copies of systems at different temperatures into a thermal contact. We solve the problem for the relativistic systems that are described by the energy-momentum of a perfect hydro with general equation of state (EOS). In particular, we examine several simple examples: a hydro with a linear EOS, a holographic CFT perturbed by a relevant operator and a barotropic fluid, i.e., P = P(E). Our studies suggest that the formation of steady state is a universal result of the hydro regime regardless of the kind of fluid.Comment: 1+17 page

Geometric RG Flow

We define geometric RG flow equations that specify the scale dependence of the renormalized effective action Gamma[g] and the geometric entanglement entropy S[x] of a QFT, considered as functionals of the background metric g and the shape x of the entanglement surface. We show that for QFTs with AdS duals, the respective flow equations are described by Ricci flow and mean curvature flow. For holographic theories, the diffusion rate of the RG flow is much larger, by a factor R_{AdS}^2/\ell_s^2, than the RG resolution length scale. To derive our results. we employ the Hamilton-Jacobi equations that dictate the dependence of the total bulk action and the minimal surface area on the geometric QFT boundary data.Comment: 20 pages, 3 figure

Adventures in Holography

In this thesis, inspired by the holographic theories, we study a variety of interesting problems in gravity, condensed matter and cosmology. First, we explore the entanglement entropy of a general region in a theory of quantum gravity using holographic calculations. In particular, we use holographic entanglement entropy prescription of Ryu-Takayanagi in the context of the Randall-Sundrum 2 model with considering three kind of gravity theory in the bulk: the Einstein gravity, the general f(R) gravity and the Gauss-Bonnet gravity. Showing the leading term is given by the usual Bekenstein-Hawking formula, we confirm the conjecture by Bianchi and Myers for this theory. Further, we calculate the first subleading term to entanglement entropy and show that they agree with the Wald entropy up to the extrinsic curvature terms. Then, we study the holographic dual of what is known as quantum Hall ferromagnetism in condensed matter theory. This phenomenon, which has been observed in graphene sam-ples by applying strong magnetic field, is the emergence of energy gaps and Hall plateaus at integer filling fractions due to occurrence of spontaneous symmetry breaking. This effect is partially understood with certain perturbative calculations at weak coupling. The question is then whether this feature survives in a strongly coupled system as well. To address this question, we apply a well-established string theory dual, namely the D3-D5 system. In this framework, coincident D5 and D7-branes are embedded in the AdS5 × S5 background of the D3-branes. Within this holographic set-up and through the numerical calculations, we investigate the possibility of spontaneous symmetry breaking and find interesting phase transitions at finite temperature. Finally, we introduce a holographic description of our four-dimensional universe through a “brane world” scenario known as the Dvali-Gabadadze-Porrati (DGP) construction, where the brane refers to our universe embedded in a bulk space-time with five or more dimensions. In fact, we examine the DGP model as a theory of five-dimensional Einstein gravity coupled to four-dimensional branes while we assume five-dimensional spherical black hole metric in the bulk. Then, we study the phenomenological viability of the brane around this five-dimensional black hole. Further, we relate bulk, brane, and black hole parameters and the observational constraints on them. We find that viable solutions are indeed possible, hence we propose a holographic origin for the big bang. In particular, we suggest that our four-dimensional brane emerges from the gravitational collapse of matter in five dimensions which avoids the big bang singularity

Non-analyticity of holographic Rényi entropy in Lovelock gravity

We compute holographic Rényi entropies for spherical entangling surfaces on the boundary while considering third order Lovelock gravity with negative cosmological constant in the bulk. Our study shows that third order Lovelock black holes with hyperbolic event horizon are unstable, and at low temperatures those with smaller mass are favoured, giving rise to first order phase transitions in the bulk. We determine regions in the Lovelock parameter space in arbitrary dimensions, where bulk phase transitions happen and where boundary causality constraints are met. We show that each of these points corresponds to a dual boundary conformal field theory whose Rényi entropy exhibits a kink at a certain critical index n.This research was supported in part by the Icelandic Research Fund under contracts 163419-051 and 163422-051, and by grants from the University of Iceland Research Fund.Peer Reviewe