scholarly journals Page curve for entanglement negativity through geometric evaporation

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Jaydeep Kumar Basak ◽  
Debarshi Basu ◽  
Vinay Malvimat ◽  
Himanshu Parihar ◽  
Gautam Sengupta
Keyword(s):  
Black Hole ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Mixed State ◽  
Dimensional Reduction ◽  
Matrix Theory ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Btz Black Hole ◽  
Diagrammatic Technique

We compute the entanglement negativity for various pure and mixed state configurations in a bath coupled to an evaporating two dimensional non-extremal Jackiw-Teitelboim (JT) black hole obtained through the partial dimensional reduction of a three dimensional BTZ black hole. Our results exactly reproduce the analogues of the Page curve for the entanglement negativity which were recently determined through diagrammatic technique developed in the context of random matrix theory.

Chiral modular bootstrap

2019 ◽  
Vol 34 (28) ◽  
pp. 1950168 ◽  
Author(s):  
M. Ashrafi
Keyword(s):  
Black Hole ◽  
Upper Bound ◽  
Three Dimensional ◽  
Conformal Weight ◽  
Two Dimensional ◽  
Btz Black Hole ◽  
Conformal Field ◽  
Dimensional Gravity ◽  
Large Spin ◽  
Dimension Ratio

Using modular bootstrap we show the lightest primary fields of a unitary compact two-dimensional conformal field theory (with [Formula: see text], [Formula: see text]) has a conformal weight [Formula: see text]. This implies that the upper bound on the dimension of the lightest primary fields depends on their spin. In particular if the set of lightest primary fields includes extremal or near extremal states whose spin to dimension ratio [Formula: see text], the corresponding dimension is [Formula: see text]. From AdS/CFT correspondence, we obtain an upper bound on the spectrum of black hole in three-dimensional gravity. Our results show that if the first primary fields have large spin, the corresponding three-dimensional gravity has extremal or near extremal BTZ black hole.

scholarly journals AdS3 wormholes from a modular bootstrap

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Jordan Cotler ◽  
Kristan Jensen
Keyword(s):  
Low Temperature ◽  
Path Integral ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Central Charge ◽  
Three Dimensional ◽  
Single Instance ◽  
Dimensional Gravity ◽  
3D Gravity

Abstract In recent work we computed the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. Here we employ a modular bootstrap to show that the amplitude is completely fixed by consistency conditions and a few basic inputs from gravity. This bootstrap is notably for an ensemble of CFTs, rather than for a single instance. We also compare the 3d gravity result with the Narain ensemble. The former is well-approximated at low temperature by a random matrix theory ansatz, and we conjecture that this behavior is generic for an ensemble of CFTs at large central charge with a chaotic spectrum of heavy operators.

scholarly journals AdS3 gravity and random CFT

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Jordan Cotler ◽  
Kristan Jensen
Keyword(s):  
Random Matrix ◽  
Linear Growth ◽  
Matrix Theory ◽  
Three Dimensional ◽  
Energy Limit ◽  
Spectral Form ◽  
Btz Black Hole ◽  
Virasoro Symmetry ◽  
Dimensional Gravity ◽  
Matrix Ensemble

Abstract We compute the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. These are Euclidean wormholes, which smoothly interpolate between two asymptotically Euclidean AdS3 regions with torus boundary. From our results we obtain the spectral correlations between BTZ black hole microstates near threshold, as well as extract the spectral form factor at fixed momentum, which has linear growth in time with small fluctuations around it. The low-energy limit of these correlations is precisely that of a double-scaled random matrix ensemble with Virasoro symmetry. Our findings suggest that if pure three-dimensional gravity has a holographic dual, then the dual is an ensemble which generalizes random matrix theory.

scholarly journals Random matrix theory for complexity growth and black hole interiors

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Arjun Kar ◽  
Lampros Lamprou ◽  
Moshe Rozali ◽  
James Sully
Keyword(s):  
Black Hole ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Linear Growth ◽  
Matrix Theory ◽  
Main Tool ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Maximal Volume ◽  
Quantum Theories

Abstract We study a precise and computationally tractable notion of operator complexity in holographic quantum theories, including the ensemble dual of Jackiw-Teitelboim gravity and two-dimensional holographic conformal field theories. This is a refined, “microcanonical” version of K-complexity that applies to theories with infinite or continuous spectra (including quantum field theories), and in the holographic theories we study exhibits exponential growth for a scrambling time, followed by linear growth until saturation at a time exponential in the entropy — a behavior that is characteristic of chaos. We show that the linear growth regime implies a universal random matrix description of the operator dynamics after scrambling. Our main tool for establishing this connection is a “complexity renormalization group” framework we develop that allows us to study the effective operator dynamics for different timescales by “integrating out” large K-complexities. In the dual gravity setting, we comment on the empirical match between our version of K-complexity and the maximal volume proposal, and speculate on a connection between the universal random matrix theory dynamics of operator growth after scrambling and the spatial translation symmetry of smooth black hole interiors.

scholarly journals From the BTZ black hole to JT gravity: geometrizing the island

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Evita Verheijden ◽  
Erik Verlinde
Keyword(s):  
Black Hole ◽  
Finite Temperature ◽  
Three Dimensional ◽  
Point Of View ◽  
Geometric Representation ◽  
Two Dimensional ◽  
Btz Black Hole ◽  
Island Region ◽  
Dimensional Spacetime ◽  
Over Time

Abstract We study the evaporation of two-dimensional black holes in JT gravity from a three-dimensional point of view. A partial dimensional reduction of AdS3 in Poincaré coordinates leads to an extremal 2D black hole in JT gravity coupled to a ‘bath’: the holographic dual of the remainder of the 3D spacetime. Partially reducing the BTZ black hole gives us the finite temperature version. We compute the entropy of the radiation using geodesics in the three-dimensional spacetime. We then focus on the finite temperature case and describe the dynamics by introducing time-dependence into the parameter controlling the reduction. The energy of the black hole decreases linearly as we slowly move the dividing line between black hole and bath. Through a re-scaling of the BTZ parameters we map this to the more canonical picture of exponential evaporation. Finally, studying the entropy of the radiation over time leads to a geometric representation of the Page curve. The appearance of the island region is explained in a natural and intuitive fashion.

scholarly journals Random Matrix Theory and Three-Dimensional QCD

1994 ◽  
Vol 73 (17) ◽  
pp. 2288-2291 ◽  
Author(s):  
J. J. M. Verbaarschot ◽  
I. Zahed
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Three Dimensional

scholarly journals A MODEL OF TWO-DIMENSIONAL TURBULENCE USING RANDOM MATRIX THEORY

2002 ◽  
Vol 17 (23) ◽  
pp. 1539-1550 ◽  
Author(s):  
SAVITRI V. IYER ◽  
S. G. RAJEEV
Keyword(s):  
Maximum Entropy ◽  
Random Matrices ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Simple Formula ◽  
Matrix Theory ◽  
Inviscid Flow ◽  
Two Dimensional ◽  
Cylindrically Symmetric ◽  
Vortex Field

We derive a formula for the entropy of two-dimensional incompressible inviscid flow, by determining the volume of the space of vorticity distributions with fixed values for the moments Qk = ∫ ω(x)kd2x. This space is approximated by a sequence of spaces of finite volume, by using a regularization of the system that is geometrically natural and connected with the theory of random matrices. By taking the limit we get a simple formula for the entropy of a vortex field. We predict vorticity distributions of maximum entropy with given mean vorticity and enstrophy; we also predict the cylindrically symmetric vortex field with maximum entropy. This could be an approximate description of a hurricane.

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