Bra-ket wormholes in gravitationally prepared states

Yiming Chen; Victor Gorbenko; Juan Maldacena

doi:10.1007/jhep02(2021)009

Bra-ket wormholes in gravitationally prepared states

Journal of High Energy Physics ◽

10.1007/jhep02(2021)009 ◽

2021 ◽

Vol 2021 (2) ◽

Cited By ~ 3

Author(s):

Yiming Chen ◽

Victor Gorbenko ◽

Juan Maldacena

Keyword(s):

Hyperbolic Space ◽

Path Integral ◽

Flat Space ◽

Low Energy ◽

Two Dimensional ◽

De Sitter ◽

Euclidean Case ◽

Fine Grained ◽

Entropy Formula ◽

First Case

Abstract We consider two dimensional CFT states that are produced by a gravitational path integral.As a first case, we consider a state produced by Euclidean AdS2 evolution followed by flat space evolution. We use the fine grained entropy formula to explore the nature of the state. We find that the naive hyperbolic space geometry leads to a paradox. This is solved if we include a geometry that connects the bra with the ket, a bra-ket wormhole. The semiclassical Lorentzian interpretation leads to CFT state entangled with an expanding and collapsing Friedmann cosmology.As a second case, we consider a state produced by Lorentzian dS2 evolution, again followed by flat space evolution. The most naive geometry also leads to a similar paradox. We explore several possible bra-ket wormholes. The most obvious one leads to a badly divergent temperature. The most promising one also leads to a divergent temperature but by making a projection onto low energy states we find that it has features that look similar to the previous Euclidean case. In particular, the maximum entropy of an interval in the future is set by the de Sitter entropy.

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Exact expressions for n-point maximal U(1)Y-violating integrated correlators in SU(N) $$ \mathcal{N} $$ = 4 SYM

Journal of High Energy Physics ◽

10.1007/jhep11(2021)132 ◽

2021 ◽

Vol 2021 (11) ◽

Author(s):

Daniele Dorigoni ◽

Michael B. Green ◽

Congkao Wen

Keyword(s):

Modular Forms ◽

Free Field ◽

Perturbation Expansion ◽

Flat Space ◽

Low Energy ◽

Two Dimensional ◽

Dimensional Lattice ◽

Yang Mills ◽

Infinite Sums

Abstract The exact expressions for integrated maximal U(1)Y violating (MUV) n-point correlators in SU(N) $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory are determined. The analysis generalises previous results on the integrated correlator of four superconformal primaries and is based on supersymmetric localisation. The integrated correlators are functions of N and τ = θ/(2π) + 4πi/$$ {g}_{YM}^2 $$ g YM 2 , and are expressed as two-dimensional lattice sums that are modular forms with holomorphic and anti-holomorphic weights (w, −w) where w = n − 4. The correlators satisfy Laplace-difference equations that relate the SU(N+1), SU(N) and SU(N−1) expressions and generalise the equations previously found in the w = 0 case. The correlators can be expressed as infinite sums of Eisenstein modular forms of weight (w, −w). For any fixed value of N the perturbation expansion of this correlator is found to start at order ($$ {g}_{YM}^2 $$ g YM 2 N)w. The contributions of Yang-Mills instantons of charge k > 0 are of the form qkf(gYM), where q = e2πiτ and f(gYM) = O($$ {g}_{YM}^{-2w} $$ g YM − 2 w ) when $$ {g}_{YM}^2 $$ g YM 2 ≪ 1. Anti-instanton contributions have charge k < 0 and are of the form $$ {\overline{q}}^{\left|k\right|}\hat{f}\left({g}_{YM}\right) $$ q ¯ k f ̂ g YM , where $$ \hat{f}\left({g}_{YM}\right)=O\left({g}_{YM}^{2w}\right) $$ f ̂ g YM = O g YM 2 w when $$ {g}_{YM}^2 $$ g YM 2 ≪ 1. Properties of the large-N expansion are in agreement with expectations based on the low energy expansion of flat-space type IIB superstring amplitudes. We also comment on the identification of n-point free-field MUV correlators with the integrands of (n − 4)-loop perturbative contributions to the four-point correlator. In particular, we emphasise the important rôle of SL(2, ℤ)-covariance in the construction.

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KINEMATICS OF FLOWS ON CURVED, DEFORMABLE MEDIA

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887809003746 ◽

2009 ◽

Vol 06 (04) ◽

pp. 645-666 ◽

Cited By ~ 18

Author(s):

ANIRVAN DASGUPTA ◽

HEMWATI NANDAN ◽

SAYAN KAR

Keyword(s):

Hyperbolic Space ◽

Initial Conditions ◽

Three Dimensional ◽

Flat Space ◽

Singular Solutions ◽

Geodesic Flows ◽

Two Dimensional ◽

Singular Behavior ◽

Deformable Media ◽

Raychaudhuri Equations

Kinematics of geodesic flows on specific, two-dimensional, curved surfaces (the sphere, hyperbolic space and the torus) are investigated by explicitly solving the evolution (Raychaudhuri) equations for the expansion, shear and rotation, for a variety of initial conditions. For flows on the sphere and on hyperbolic space, we show the existence of singular (within a finite value of the time parameter) as well as non-singular solutions. We illustrate our results through a phase diagram which demonstrates under which initial conditions (or combinations thereof) we end up with a singularity in the congruence and when, if at all, we can obtain non-singular solutions for the kinematic variables. Our analysis portrays the differences which arise due to positive or negative curvature and also explores the role of rotation in controlling singular behavior. Subsequently, we move on to geodesic flows on two-dimensional spaces with varying curvature. As an example, we discuss flows on a torus. Characteristic oscillatory features, dependent on the ratio of the two radii of the torus, emerge in the solutions for the expansion, shear and rotation. Singular (within a finite time) and non-singular behavior of the solutions are also discussed. Finally, we conclude with a generalization to three-dimensional spaces of constant curvature, a summary of some of the generic features obtained and a comparison of our results with those for flows in flat space.

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New boundary conditions for AdS2

Journal of High Energy Physics ◽

10.1007/jhep12(2020)020 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Victor Godet ◽

Charles Marteau

Keyword(s):

Boundary Conditions ◽

Path Integral ◽

Flat Space ◽

Low Energy ◽

Asymptotic Symmetry ◽

Coadjoint Action ◽

Matrix Ensemble ◽

Virasoro Group ◽

Random Matrix Ensemble ◽

Extremal Black Holes

Abstract We describe new boundary conditions for AdS2 in Jackiw-Teitelboim gravity. The asymptotic symmetry group is enhanced to Diff(S1) ⋉ C∞(S1) whose breaking to SL(2, ℝ) × U(1) controls the near-AdS2 dynamics. The action reduces to a boundary term which is a generalization of the Schwarzian theory and can be interpreted as the coadjoint action of the warped Virasoro group. This theory reproduces the low-energy effective action of the complex SYK model. We compute the Euclidean path integral and derive its relation to the random matrix ensemble of Saad, Shenker and Stanford. We study the flat space version of this action, and show that the corresponding path integral also gives an ensemble average, but of a much simpler nature. We explore some applications to near-extremal black holes.

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SEMICLASSICAL (QUANTUM FIELD THEORY) AND QUANTUM (STRING) DE SITTER REGIMES: NEW RESULTS

International Journal of Modern Physics D ◽

10.1142/s0218271807010596 ◽

2007 ◽

Vol 16 (06) ◽

pp. 1053-1074 ◽

Cited By ~ 4

Author(s):

A. BOUCHAREB ◽

M. RAMÓN MEDRANO ◽

N. G. SÁNCHEZ

Keyword(s):

Phase Transition ◽

Black Hole ◽

Emission Cross Section ◽

Hubble Constant ◽

Flat Space ◽

De Sitter Space ◽

Space Time ◽

De Sitter ◽

Entropy Formula ◽

New Phase

We compute the quantum string entropy S s (m, H) from the microscopic string density of states ρ s (m, H) of mass m in de Sitter space–time. We find for high m (high Hm → c/α') a new phase transition at the critical string temperature T s = (1/2πk B )L cl c2/α', higher than the flat space (Hagedorn) temperature t s (L cl = c/H, the Hubble constant H acts at the transition, producing a smaller string constant α' and thus, a higher tension). T s is the precise quantum dual of the semiclassical (QFT Hawking–Gibbons) de Sitter temperature T sem = ħ c/(2πk B L cl ). By precisely identifying the semiclassical and quantum (string) de Sitter regimes, we find a new formula for the full de Sitter entropy S sem (H), as a function of the usual Bekenstein–Hawking entropy [Formula: see text]. For L cl ≫ ℓ Planck , i.e. for low [Formula: see text] is the leading term, but for high H near c/ℓ Planck , a new phase transition operates and the whole entropy S sem (H) is drastically different from the Bekenstein–Hawking entropy [Formula: see text]. We compute the string quantum emission cross-section σ string by a black hole in de Sitter (or asymptotically de Sitter) space–time (bhdS). For T sem bhdS ℓ T s (early evaporation stage), it shows the QFT Hawking emission with temperature T sem bhdS (semiclassical regime). For T sem bhdS → T s , σ string exhibits a phase transition into a string de Sitter state of size [Formula: see text], [Formula: see text], and string de Sitter temperature T s . Instead of featuring a single pole singularity in the temperature (Carlitz transition), it features a square root branch point (de Vega–Sanchez transition). New bounds on the black hole radius r g emerge in the bhdS string regime: it can become r g = L s /2, or it can reach a more quantum value, r g = 0.365 ℓ s .

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Regions-based Two-dimensional Continua: The Euclidean Case

10.1093/oso/9780198712749.003.0005 ◽

2018 ◽

Author(s):

Geoffrey Hellman ◽

Stewart Shapiro

Keyword(s):

Mathematical Induction ◽

Dimensional Case ◽

Two Dimensional ◽

Entire Space ◽

Euclidean Case ◽

Free Basis ◽

One Dimensional ◽

Archimedean Property ◽

The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

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Complex magnetism of the two-dimensional antiferromagnetic Ge2F: from a Néel spin-texture to a potential antiferromagnetic skyrmion

RSC Advances ◽

10.1039/d0ra09678d ◽

2021 ◽

Vol 11 (15) ◽

pp. 8654-8663

Author(s):

Fatima Zahra Ramadan ◽

Flaviano José dos Santos ◽

Lalla Btissam Drissi ◽

Samir Lounis

Keyword(s):

Density Functional Theory ◽

Magnetic Properties ◽

Density Functional ◽

Low Energy ◽

Two Dimensional ◽

Functional Theory ◽

2D Material ◽

Energy Models ◽

Spin Texture

Based on density functional theory combined with low-energy models, we explore the magnetic properties of a hybrid atomic-thick two-dimensional (2D) material made of germanene doped with fluorine atoms in a half-fluorinated configuration (Ge2F).

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Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽

10.3390/math9050531 ◽

2021 ◽

Vol 9 (5) ◽

pp. 531

Author(s):

Pedro Pablo Ortega Palencia ◽

Ruben Dario Ortiz Ortiz ◽

Ana Magnolia Marin Ramirez

Keyword(s):

Negative Curvature ◽

Dimensional Space ◽

Center Of Mass ◽

Simple Expression ◽

Two Dimensional ◽

Constant Negative Curvature ◽

Euclidean Case ◽

System Of Particles ◽

Material Points ◽

The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

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Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory

Journal of High Energy Physics ◽

10.1007/jhep12(2020)189 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Fridrich Valach ◽

Donald R. Youmans

Keyword(s):

Quantum Mechanics ◽

Partition Function ◽

Gauge Group ◽

Path Integral ◽

Coadjoint Orbits ◽

Two Dimensional ◽

Edge States ◽

Class Constraint ◽

Action Functional ◽

Bf Theory

Abstract We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

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