In the study of three-dimensional flat holography, the BMS field theory manifests the infinite-dimensional BMS$_3$ symmetry, a powerful tool in elucidating numerous universal phenomena. This paper explores a certain low-temperature limit of the BMS field theory. The primary focus lies in the calculation of the thermal correction to the Rényi entropy of the single interval on the cylinder from the replica trick and the uniformizing map. As a double check, an alternative method calculating the entanglement entropy is introduced, with the entanglement first law and the modular Hamiltonian.
Using Rindler method we derive the logarithmic correction to the entanglement entropy of a two dimensional BMS-invariant field theory (BMSFT). In particular, we present a general formula for extraction of the logarithmic corrections to both the thermal and the entanglement entropies. We also present a CFT formula related to the logarithmic correction of the BTZ inner horizon entropy which results in our formula after taking appropriate limit.
We construct the characters for the highest weight representations of the 3d Bondi-Metzner-Sachs (BMS$_3$) algebra. We then use these to construct the partition function and show how to use BMS modular transformations to obtain a density of primary states. The entropy thus obtained accounts for the principle part of the entropy obtained from the BMS-Cardy formula. This suggests that BMS primaries capture most of the entropy of Flat Space Cosmologies, which are the flatspace analogues of BTZ black holes in AdS$_3$. We reproduce our character formula by looking at singular limits from 2d CFT cha…
According to flat/Bondi-Metzner-Sachs invariant field theories (BMSFT) correspondence, asymptotically flat spacetimes in $(d+1)$-dimensions are dual to $d$-dimensional BMSFTs. In this duality, similar to the Ryu-Takayanagi proposal in the AdS/CFT correspondence, the entanglement entropy of subsystems in the field theory side is given by the area of some particular surfaces in the gravity side. In this paper we find the holographic counterpart of the first law of entanglement entropy (FLEE) in a two-dimensional BMSFT. We show that FLEE for the BMSFT perturbed states which are descried by three-…
Near the horizon, the obvious symmetries of a black hole spacetime---the horizon-preserving diffeomorphisms---are enhanced to a larger symmetry group with a BMS${}_3$ algebra. Using dimensional reduction and covariant phase space techniques, I investigate this augmented symmetry, and show that it is strong enough to determine the black hole entropy.
In an earlier short paper [Phys.\ Rev.\ Lett.\ 120 (2018) 101301, arXiv:1702.04439], I argued that the horizon-preserving diffeomorphisms of a generic black hole are enhanced to a larger BMS${}_3$ symmetry, which is powerful enough to determine the Bekenstein-Hawking entropy. Here I provide details and extensions of that argument, including a loosening of horizon boundary conditions and a more thorough treatment of dimensional reduction and meaning of a "near-horizon symmetry."
Previously we have studied the Generalized Minimal Massive Gravity (GMMG) in asymptotically $AdS_3$ background, and have shown that the theory is free of negative-energy bulk modes. Also we have shown GMMG avoids the aforementioned bulk-boundary unitarity clash. Here instead of $AdS_3$ space we consider asymptotically flat space, and study this model in the flat limit. The dual field theory of GMMG in the flat limit is a $BMS_3$ invariant field theory, dubbed (BMSFT) and we have BMS algebra asymptotically instead of Virasoro algebra. In fact here we present an evidence for this claim. Entangle…
In this paper, we develop a perturbation formulation to calculate the single interval higher spin R$\acute{e}$nyi and entanglement entropy for two dimensional conformal field theory with $\mathcal{W}_{\infty}(λ)$ symmetry. The system is at finite temperature and is deformed by higher spin chemical potential. We manage to compute higher spin R$\acute{e}$nyi entropy with various spin deformations up to order $\mathcal{O}(μ^2)$. For spin 3 deformation, we calculate exact higher spin R$\acute{e}$nyi entropy up to $\mathcal{O}(μ^4)$. When $λ=3$, in the large $c$ limit, we find perfect match with tr…
BMS symmetry, which is the asymptotic symmetry at null infinity of flat spacetime, is an important input for flat holography. In this paper, we give a holographic calculation of entanglement entropy and Rényi entropy in three dimensional Einstein gravity and Topologically Massive Gravity. The geometric picture for the entanglement entropy is the length of a spacelike geodesic which is connected to the interval at null infinity by two null geodesics. The spacelike geodesic is the fixed points of replica symmetry, and the null geodesics are along the modular flow. Our strategy is to first reform…
We explore the holographic principle in the context of asymptotically flat spacetimes. In analogy with the AdS/CFT scenario we analyse the asympotically symmetry group of this class of spacetimes, the so called Bondi-Metzner-Sachs (BMS) group. We apply the covariant entropy bound to relate bulk entropy to boundary symmetries and find a quite different picture with respect to the asymptotically AdS case. We then derive the covariant wave equations for fields carrying BMS representations to investigate the nature of the boundary degrees of freedom. We find some similarities with 't Hooft S-matri…
Recently a general prescription for determining the vacuum modular flow generator and the corresponding modular Hamiltonian in the BMS-invariant field theories (BMSFTs) have provided by Apolo et. al \cite{Apolo}. According to this paper Einstein gravity in asymptotically flat three-dimensional spacetimes is dual to a BMSFT. In the present paper we extend this study to the generalized minimal massive gravity model (GMMG). So we study some aspects of $Flat_3/BMSFT$ holography in the framework of this model. We derive the modular Hamiltonian for single intervals in thermal and non-thermal BMSFTs …
We apply the new fall of conditions presented in the paper \cite{10} on asymptotically flat spacetime solutions of Chern-Simons-like theories of gravity. We show that the considered fall of conditions asymptotically solve equations of motion of generalized minimal massive gravity. We demonstrate that there exist two type of solutions, one of those is trivial and the others are non-trivial. By looking at non-trivial solutions, for asymptotically flat spacetimes in the generalized minimal massive gravity, in contrast to Einstein gravity, cosmological parameter can be non-zero. We obtain the cons…
In this paper we perform the Hamiltonian reduction of the action for three-dimensional Einstein gravity with vanishing cosmological constant using the Chern-Simons formulation and Bondi-van der Burg-Metzner-Sachs (BMS) boundary conditions. An equivalent formulation of the boundary action is the geometric action on BMS$_3$ coadjoint orbits, where the orbit representative is identified as the bulk holonomy. We use this reduced action to compute one-loop contributions to the torus partition function of all BMS$_3$ descendants of Minkowski spacetime and cosmological solutions in flat space. We the…
Black hole entropy, denoted by N, in (semi)classical limit is infinite. This scaling reveals a very important information about the qubit degrees of freedom that carry black hole entropy. Namely, the multiplicity of qubits scales as N, whereas their energy gap and their coupling as 1/N. Such a behavior is indeed exhibited by Bogoliubov-Goldstone degrees of freedom of a quantum-critical state of N soft gravitons (a condensate or a coherent state) describing the black hole quantum portrait. They can be viewed as the Goldstone modes of a broken symmetry acting on the graviton condensate. In this …
We study several aspects of holographic entanglement in two models known as flat$_3$/BMSFT and (W)AdS$_3$/WCFT. These are two examples of holography beyond AdS/CFT where the the boundary field theories are not Lorentz invariant but still feature an infinite set of local symmetries. In the first example, BMS-invariant field theories (BMSFTs) are conjectured to provide a holographic description of quantum gravity in asymptotically flat three-dimensional spacetimes; while in the second example, warped conformal field theories (WCFTs) are proposed to describe quantum gravity in warped AdS$_3$ or A…
We propose a holographic entanglement entropy prescription for general states and regions in two models of holography beyond AdS/CFT known as flat$_3$/BMSFT and (W)AdS$_3$/WCFT. Flat$_3$/BMSFT is a candidate of holography for asymptotically flat three-dimensional spacetimes, while (W)AdS$_3$/WCFT is relevant in the study of black holes in the real world. In particular, the boundary theories are examples of quantum field theories that feature an infinite dimensional symmetry group but break Lorentz invariance. Our holographic entanglement entropy proposal is given by the area of a swing surface…
A logarithmic but divergent term usually appears in the computation of entanglement entropy circumferencing a black hole, while the leading quantum correction to the Bekenstein-Hawking entropy also takes the logarithmic form. A quench model of CFT within finite Euclidean time was proposed in the \cite{Kuwakino:2014nra} to regard this logarithmic term as entanglement between radiation and the black hole, and this proposal was justified by the alternative sign for $n$-partite quantum information. However, this preliminary form suffers from the notorious divergence at its low temperature limit. I…
We provide a first derivation of the Bekenstein-Hawking entropy of 3d flat cosmological horizons in terms of the counting of states in a dual field theory. These horizons appear in the shifted-boost orbifold of R^{1,2}, the flat limit of non-extremal rotating BTZ black holes. These 3d geometries carry non-zero charges under the asymptotic symmetry algebra of R^{1,2}, the 3d Bondi-Metzner-Sachs (BMS3) algebra. The dual theory has the symmetries of the 2d Galilean Conformal Algebra, a contraction of two copies of the Virasoro algebra, which is isomorphic to BMS3. We study flat holography as a li…
We consider BTZ black holes and flat space cosmologies in generic higher derivative gravity theories in 2+1 dimensions. Our goal is to prove the match between the bulk Iyer-Wald entropy and the field theory entropy for various symmetry algebras (CFT$_2$, Warped CFT$_2$, BMS$_3$). We also discuss phase transitions in higher curvature theories, and argue that, in the flat case, there is strictly speaking no phase transition in the grand canonical ensemble.
We consider conformal field theories in 1+1 dimensions with W-algebra symmetries, deformed by a chemical potential μfor the spin-three current. We show that the order μ^2 correction to the Re'nyi and entanglement entropies of a single interval in the deformed theory, on the infinite spatial line and at finite temperature, is universal. The correction is completely determined by the operator product expansion of two spin-three currents, and by the expectation values of the stress tensor, its descendants and its composites, evaluated on the n-sheeted Riemann surface branched along the interval. …
The topological structures of a $ϕ^6$ theory with multi-field are studied. The $ϕ^6$ theory is interesting because it is a theory that allows the shrinkage of topological structures generating double-kink or even multi-kink configurations. In this work, we consider and study the solutions of a two real scalar fields model. To reach our purpose, we investigate the BPS properties of the fields using the approach proposed by Bogomol'nyi-Prasad-Sommerfield. Using the BPS energy density, the differential configurational entropy (DCE) of the BPS structures is studied. The result of the DCE indicates…
The asymptotically flat structure of $\mathcal{N}=(2,0)$ supergravity in three spacetime dimensions is explored. The asymptotic symmetries are spanned by an extension of the super-BMS$_3$ algebra, with two independent $\hat{u}(1)$ currents of electric and magnetic type. These currents are associated to $U(1)$ fields being even and odd under parity, respectively. Remarkably, although the $U(1)$ fields do not generate a backreaction on the metric, they provide nontrivial Sugawara-like contributions to the BMS$_3$ generators, and hence to the energy and the angular momentum. The entropy of flat c…
The area of a cross-sectional cut $Σ$ of future null infinity ($\mathcal{I}^+$) is infinite. We define a finite, renormalized area by subtracting the area of the same cut in any one of the infinite number of BMS-degenerate classical vacua. The renormalized area acquires an anomalous dependence on the choice of vacuum. We relate it to the modular energy, including a soft graviton contribution, of the region of $\mathcal{I}^+$ to the future of $Σ$. Under supertranslations, the renormalized area shifts by the supertranslation charge of $Σ$. In quantum gravity, we conjecture a bound relating the r…
We propose a covariant prescription to compute holographic entanglement entropy and Poincare blocks (Global BMS blocks) in the context of three-dimensional Einstein gravity in flat space. We first present a prescription based on worldline methods in the probe limit, inspired by recent analog calculations in AdS/CFT. Building on this construction, we propose a full extrapolate dictionary and use it to compute holographic correlators and blocks away from the probe limit.
In this paper we present a new set of asymptotic boundary conditions for Einstein gravity in 2+1 dimensions with vanishing cosmological constant that are a generalization of the Barnich-Comp{è}re boundary conditions gr-qc/0610130. These new boundary conditions lead to an asymptotic symmetry algebra that is generated by a $\mathfrak{bms}_3$ algebra and two affine $\hat{\mathfrak{u}}(1)$ current algebras. We then apply these boundary conditions to Topologically Massive Gravity (TMG) and determine how the presence of the gravitational Chern-Simons term affects the central extensions of the asympt…
We consider a six-dimensional solitonic string solution described by a conformal chiral null model with non-trivial $N=4$ superconformal transverse part. It can be interpreted as a five-dimensional dyonic solitonic string wound around a compact fifth dimension. The conformal model is regular with the short-distance (`throat') region equivalent to a WZW theory. At distances larger than the compactification scale the solitonic string reduces to a dyonic static spherically-symmetric black hole of toroidally compactified heterotic string. The new four-dimensional solution is parameterised by five …
In this work, we study the quantum entanglement and compute entanglement entropy in de Sitter space for a bipartite quantum field theory driven by axion originating from ${\bf Type~ IIB}$ string compactification on a Calabi Yau three fold (${\bf CY^3}$) and in presence of ${\bf NS5}$ brane. For this compuation, we consider a spherical surface ${\bf S}^2$, which divide the spatial slice of de Sitter (${\bf dS_4}$) into exterior and interior sub regions. We also consider the initial choice of vaccum to be Bunch Davies state. First we derive the solution of the wave function of axion in a hyperbo…
In this work, we study the phenomena of quantum entanglement by computing de Sitter entanglement entropy from von Neumann measure. For this purpose we consider a bipartite quantum field theoretic setup in presence of axion originating from ${\bf Type~ II~B}$ string theory. We consider the initial vacuum to be CPT invariant non-adiabatic $α$ vacua state under ${\bf SO(1,4)}$ ismometry, which is characterized by a real one-parameter family. To implement this technique we use a ${\bf S^2}$ which divide the de Sitter into two exterior and interior sub-regions. First, we derive the wave function of…
We study the asymptotically flat rotating hairy black hole solution of a three-dimensional gravity theory which is given by taking the flat-space limit (zero cosmological constant limit) of new massive gravity. We propose that the dual field theory of the flat-space limit of new massive gravity can be described by a contracted conformal field theory which is invariant under the action of the BMS$_{3}$ group. Using the flat/contracted conformal field theory correspondence, we construct a stress tensor which yields the conserved charges of the asymptotically flat black hole solution. We check th…
In this work, our prime objective is to study non-locality and long-range effects of two-body correlation using quantum entanglement from the various information-theoretic measures in the static patch of de Sitter space using a two-body Open Quantum System (OQS). The OQS is described by a system of two entangled atoms, surrounded by a thermal bath, which is modelled by a massless probe scalar field. Firstly, we partially trace over the bath field and construct the Gorini Kossakowski Sudarshan Lindblad (GSKL) master equation, which describes the time evolution of the reduced subsystem density m…
