Related papers: Entanglement entropy and the Ricci flow
We study relation of the Ricci Flow on 3-dimensional Lie groups and 4-dimensional Ricci-flat manifolds. In particular, we construct Ricci-flat cohomogeneity one metrics with respect to 3-dimensional Lie groups.
We study the entanglement entropy between a strip region with width $2R$ and its complement in strongly coupled large-$N$ conformal field theory (CFT) on $\mathbb{R}^{1,n}$ with chemical potential and angular momentum in an thermal…
The entanglement entropy of a pure quantum state of a bipartite system is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local Hamiltonians in one…
For an ancient Ricci flow asymptotic to a compact integrable shrinker, or a Ricci flow developing a finite-time singularity modelled on the shrinker, we establish the long-time existence of a harmonic map heat flow between the Ricci flow…
Employing the Noether charge technique and Visser's Euclidean approach the entropy of the nonlinear black hole described by the perturbative solution of the system of coupled equations of the quadratic gravity and nonlinear electrodynamics…
The Ricci flow is a parabolic evolution equation in the space of Riemannian metrics of a smooth manifold. To some extent, Einstein equations give rise to a similar hyperbolic evolution. The present text is an introductory exposition to…
In this article, we establish a monotonicity formula of Hamilton type entropy along Ricci flow on compact surfaces with boundary. We also study the relation between our entropy functional and the $\mathcal{W}$-functional of Perelman type.
I show that the black hole entropy associated to an $AdS_2$ wormhole is an entanglement edge term related to a natural measure on the gauge group in the $SL(2)$ gauge theory formulation of $1+1d$ Jackiw-Teitelboim gravity. I comment on what…
The Ricci flow has been of fundamental importance in mathematics, most famously though its use as a tool for proving the Poincar\'e Conjecture and Thurston's Geometrization Conjecture. It has a parallel life in physics, arising as the first…
Black hole entropy has been shown by 't Hooft to diverge at the horizon, whereas entanglement entropy in general does not. We show that because the region near the horizon is a thermal state, entropy is linear to energy, and energy at a…
We show that the entropy resulting from the counting of microstates of non extremal black holes using field theory duals of string theories can be interpreted as arising from entanglement. The conditions for making such an interpretation…
In gravitational thermodynamics, the origin of a black hole's entropy is the topology of its instanton or constrained instanton. We prove that the entropy of an arbitrary nonrotating black hole is one quarter the sum of the products of the…
To understand an emergent spacetime is to understand the emergence of locality. Entanglement entropy is a powerful diagnostic of locality, because locality leads to a large amount of short distance entanglement. Two dimensional string…
We investigate the black hole solution to (2+1)-dimensional gravity coupled to topological matter, with a vanishing cosmological constant. We calculate the total energy, angular momentum and entropy of the black hole in this model and…
The entropy of a Ba\~nados, Teitelboim, and Zanelli black hole in topologically massive gravity had been given with the form inconsistent with the Bekenstein-Hawking entropy. In the paper, we provide a consistent statistical interpretation…
In stark contrast to lower dimensions, we produce a plethora of ancient and immortal Ricci flows in real dimension $4$ with Einstein orbifolds as tangent flows at infinity. For instance, for any $k\in\mathbb{N}_0$, we obtain continuous…
We study the attractor flow and near horizon geometry of two-charge small black holes in heterotic string theory. The Hessian of Sen's entropy function with respect to the moduli fields has standard attractor properties and shows the…
We consider the situation when a globally defined four-dimensional field system is separated on two entangled sub-systems by a dynamical (random) two-dimensional surface. The reduced density matrix averaged over ensemble of random surfaces…
In this short essay we review the arguments showing that black hole entropy is, at least in part, ``entanglement entropy", i.e., missing information contained in correlations between quantum field fluctuations inside and outside the event…
We initiate a systematic study of entanglement and Renyi entropies in the presence of gauge and gravitational anomalies in even-dimensional quantum field theories. We argue that the mixed and gravitational anomalies are sensitive to boosts…