scholarly journals Exact Holography of Massive M2-brane Theories and Entanglement Entropy

2018 ◽  
Vol 168 ◽  
pp. 07002 ◽  
Author(s):  
Dongmin Jang ◽  
Yoonbai Kim ◽  
O-Kab Kwon ◽  
D. D. Tolla
Keyword(s):  
Conformal Symmetry ◽  
Entanglement Entropy ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Abjm Theory ◽  
Source Field ◽  
Primary Operator ◽  
Dimensional Gravity ◽  
Gauge Gravity ◽  
Gravity Duality

We test the gauge/gravity duality between the N = 6 mass-deformed ABJM theory with Uk(N) × U-k(N) gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(4)=ℤk × SO(4)=ℤk isometry. Our analysis is based on the evaluation of vacuum expectation values of chiral primary operators from the supersymmetric vacua of mass-deformed ABJM theory and from the implementation of Kaluza-Klein (KK) holography to the LLM geometries. We focus on the chiral primary operator (CPO) with conformal dimension Δ = 1. The non-vanishing vacuum expectation value (vev) implies the breaking of conformal symmetry. In that case, we show that the variation of the holographic entanglement entropy (HEE) from it’s value in the CFT, is related to the non-vanishing one-point function due to the relevant deformation as well as the source field. Applying Ryu Takayanagi’s HEE conjecture to the 4-dimensional gravity solutions, which are obtained from the KK reduction of the 11-dimensional LLM solutions, we calculate the variation of the HEE. We show how the vev and the value of the source field determine the HEE.

Generalized information and entanglement entropy, gravitation and holography

2015 ◽  
Vol 30 (16) ◽  
pp. 1530039 ◽  
Author(s):  
O. Obregón
Keyword(s):  
Entanglement Entropy ◽  
Ideal Gas ◽  
Einstein Equations ◽  
Von Neumann Entropy ◽  
Nonextensive Statistical Mechanics ◽  
Von Neumann ◽  
H Theorem ◽  
Gauge Gravity ◽  
Gravity Duality ◽  
Correction Terms

A nonextensive statistical mechanics entropy that depends only on the probability distribution is proposed in the framework of superstatistics. It is based on a Γ(χ2) distribution that depends on β and also on pl. The corresponding modified von Neumann entropy is constructed; it is shown that it can also be obtained from a generalized Replica trick. We further demonstrate a generalized H-theorem. Considering the entropy as a function of the temperature and volume, it is possible to generalize the equation of state of an ideal gas. Moreover, following the entropic force formulation a generalized Newton's law is obtained, and following the proposal that the Einstein equations can be deduced from the Clausius law, we discuss on the structure that a generalized Einstein's theory would have. Lastly, we address the question whether the generalized entanglement entropy can play a role in the gauge/gravity duality. We pay attention to 2d CFT and their gravity duals. The correction terms to the von Neumann entropy result more relevant than the usual UV ones and also than those due to the area dependent AdS3 entropy which result comparable to the UV ones. Then the correction terms due to the new entropy would modify the Ryu–Takayanagi identification between the CFT entanglement entropy and the AdS entropy in a different manner than the UV ones or than the corrections to the AdS3 area dependent entropy.

scholarly journals Holographic Aspects of a Relativistic Nonconformal Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Chanyong Park
Keyword(s):  
Entanglement Entropy ◽  
Transport Coefficients ◽  
Kubo Formula ◽  
Conformal Theory ◽  
Holographic Entanglement Entropy ◽  
Black Brane Solution ◽  
Brane Solution ◽  
Gauge Gravity ◽  
Gravity Duality ◽  
Self Consistency

We study a generalD-dimensional Schwarzschild-type black brane solution of the Einstein-dilaton theory and derive, by using the holographic renormalization, its thermodynamics consistent with the geometric results. Using the membrane paradigm, we calculate the several hydrodynamic transport coefficients and compare them with the results obtained by the Kubo formula, which shows the self-consistency of the gauge/gravity duality in the relativistic nonconformal theory. In order to understand more about the relativistic non-conformal theory, we further investigate the binding energy, drag force, and holographic entanglement entropy of the relativistic non-conformal theory.

scholarly journals ENTANGLEMENT ENTROPY FROM SURFACE TERMS IN GENERAL RELATIVITY

2013 ◽  
Vol 22 (12) ◽  
pp. 1342020 ◽  
Author(s):  
ARPAN BHATTACHARYYA ◽  
ANINDA SINHA
Keyword(s):  
General Relativity ◽  
Entanglement Entropy ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Conformal Field Theories ◽  
Btz Black Hole ◽  
Conformal Field ◽  
Local Quantum ◽  
Gauge Gravity ◽  
Gravity Duality

Entanglement entropy in local quantum field theories is typically ultraviolet divergent due to short distance effects in the neighborhood of the entangling region. In the context of gauge/gravity duality, we show that surface terms in general relativity are able to capture this entanglement entropy. In particular, we demonstrate that for 1 + 1-dimensional (1 + 1d) conformal field theories (CFTs) at finite temperature whose gravity dual is Banados–Teitelboim–Zanelli (BTZ) black hole, the Gibbons–Hawking–York term precisely reproduces the entanglement entropy which can be computed independently in the field theory.

BRS ANALYSIS OF THE ENERGY MOMENTUM TENSOR IN TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (18) ◽  
pp. 1679-1684
Author(s):  
W. S. L'YI ◽  
YOUNG-JAI PARK ◽  
KEE YONG KIM ◽  
YONGDUK KIM
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Momentum Tensor ◽  
Majorana Fermion ◽  
Two Dimensional ◽  
Expectation Value ◽  
Dimensional Gravity

Majorana fermion coupled to a 2-dimensional background gravitational field is investigated by employing the BRS quantization technique. Upon introduction of a quasicon-formal map ζ determined by the Beltrami differential h, the background gravitational field amazingly disappeared leaving just the free Majorana field ψ and ghosts b, c. In this way the vacuum expectation value of the energy-momentum tensor under the background gravitational field is explicitly computed.

scholarly journals Restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry

2021 ◽  
Vol 36 (28) ◽  
pp. 2150203
Author(s):  
Ichiro Oda
Keyword(s):  
Conformal Symmetry ◽  
Goldstone Boson ◽  
Minkowski Spacetime ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Global Scale ◽  
Special Conformal Transformation ◽  
Symmetry Breakdown ◽  
Weyl Symmetry ◽  
Spontaneous Symmetry Breakdown

In this paper, we elucidate the relation between the restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry. Using a scalar–tensor gravity, we show that the restricted Weyl symmetry leads to spontaneous symmetry breakdown of a global scale symmetry when the vacuum expectation value of a scalar field takes a nonzero value. It is then shown that this spontaneous symmetry breakdown induces spontaneous symmetry breakdown of special conformal symmetry in a flat Minkowski spacetime, but the resultant Nambu–Goldstone boson is not an independent physical mode but expressed in terms of the derivative of the dilaton which is the Nambu–Goldstone boson of the global scale symmetry. In other words, the theories which are invariant under the general coordinate transformation and the restricted Weyl transformation exhibit a Nambu–Goldstone phase where both special conformal transformation and dilatation are spontaneously broken while preserving the Poincaré symmetry.

A COSMOLOGY WITH CONFORMALLY COUPLED SCALAR FIELD

1991 ◽  
Vol 06 (03) ◽  
pp. 479-486 ◽  
Author(s):  
KIN-WANG NG
Keyword(s):  
Scalar Field ◽  
Vacuum Energy ◽  
Gravitational Constant ◽  
Equations Of Motion ◽  
Conformal Symmetry ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Present Theory ◽  
De Sitter ◽  
The Universe

A theory of gravitation with a conformally coupled scalar field is considered in which the gravitational “constant” is associated with the vacuum expectation value of the scalar field. It is found that the universe will remain dominated by classical radiation unless the conformal symmetry is broken. The equations of motion thus derived bear a de Sitter phase solution, which could have an exponential growth of the cosmic scale factor with no vacuum energy. We discuss the cosmological implications of this kind of “inflation”. We also find that in the present theory the smallness of the vacuum energy for most time of the universe is due to the constancy of the gravitational “constant”.

scholarly journals Lectures on Walking Technicolor, Holography, and Gauge/Gravity Dualities

2010 ◽  
Vol 2010 ◽  
pp. 1-94 ◽  
Author(s):  
Maurizio Piai
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Phenomenological Approach ◽  
Effective Field ◽  
Coupled Models ◽  
Strongly Coupled ◽  
Five Dimensions ◽  
Weakly Coupled ◽  
Counting Rules ◽  
Gauge Gravity

Dynamical electroweak symmetry breaking is an appealing, strongly coupled alternative to the weakly coupled models based on an elementary scalar field developing a vacuum expectation value. In Sections 2 and 3 of this set of lectures, I summarize the arguments, based on low-energy phenomenology, supporting walking technicolor as a realistic realization of this idea. This pedagogical introduction to walking technicolor, and more generally to the physics of extensions of the standard model, makes extensive use of effective field theory arguments, symmetries, and counting rules. The strongly coupled nature of the underlying interactions, and the peculiar quasiconformal behavior of the theory, requires to use nonperturbative methods in order to address many fundamental questions within this framework. The recent development of gauge/gravity dualities provides an ideal set of such nonperturbative instruments. Sections 4 and 5 illustrate the potential of these techniques with two technical examples, one within the bottom-up phenomenological approach to holography in five dimensions, the other within a more systematic top-down construction derived from ten-dimensional type-IIB supergravity.

scholarly journals Fold bifurcation entangled surfaces for one-dimensional Kitaev lattice model

2021 ◽  
pp. 2150151
Author(s):  
Davood Momeni ◽  
Phongpichit Channuie
Keyword(s):  
Entanglement Entropy ◽  
One Dimensional ◽  
Dependent Part ◽  
Fold Bifurcation ◽  
Quantum Action ◽  
Kitaev Model ◽  
Gauge Gravity ◽  
Gravity Duality ◽  
Oscillatory Model ◽  
Equivalent Description

In this paper, we investigate a feasible holography with the Kitaev model using dilatonic gravity in AdS2. We propose a generic dual theory of gravity in the AdS2 and suggest that this bulk action is a suitable toy model in studying quantum mechanics in Kitaev model using gauge/gravity duality. This gives a possible equivalent description for the Kitaev model in the dual gravity bulk. Scalar and tensor perturbations are investigated in details. In the case of near AdS perturbation, we show that the geometry still “freezes” as is AdS, while the dilation perturbation decays at the AdS boundary safely. The time-dependent part of the perturbation is an oscillatory model. We discover that the dual gravity induces an effective and renormalizable quantum action. The entanglement entropy for bulk theory is computed using extremal surfaces. We prove that these surfaces have a fold bifurcation regime of criticality.

scholarly journals Entanglement and fast quantum thermalization in heavy ion collisions

2016 ◽  
Vol 31 (18) ◽  
pp. 1650110 ◽  
Author(s):  
Chiu Man Ho ◽  
Stephen D. H. Hsu
Keyword(s):  
Hilbert Space ◽  
Central Region ◽  
Heavy Ion Collisions ◽  
Degrees Of Freedom ◽  
Entanglement Entropy ◽  
Heavy Ion ◽  
Entropy Formula ◽  
Ion Collisions ◽  
Gauge Gravity ◽  
Gravity Duality

Let [Formula: see text] be subsystem of a larger system [Formula: see text] and [Formula: see text] be a typical state from the subspace of the Hilbert space [Formula: see text] satisfying an energy constraint. Then [Formula: see text] is nearly thermal. We discuss how this observation is related to fast thermalization of the central region ([Formula: see text]) in heavy ion collisions (HIC), where [Formula: see text] represents other degrees of freedom (soft modes, hard jets, collinear particles) outside of [Formula: see text]. Entanglement between the modes in [Formula: see text] and [Formula: see text] play a central role: the entanglement entropy [Formula: see text] increases rapidly in the collision. In gauge–gravity duality, [Formula: see text] is related to the area of extremal surfaces in the bulk, which can be studied using gravitational duals.

scholarly journals Entanglement entropy and the first law at third order for boosted black branes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Sabyasachi Maulik ◽  
Harvendra Singh
Keyword(s):  
Chemical Potential ◽  
Entanglement Entropy ◽  
Higher Order ◽  
Third Order ◽  
Strongly Coupled ◽  
Holographic Entanglement Entropy ◽  
Higher Order Corrections ◽  
Plane Wave Background ◽  
Gauge Gravity ◽  
Gravity Duality

Abstract Gauge/gravity duality relates an AdS black hole with uniform boost with a boosted strongly-coupled CFT at finite temperature. We study the perturbative change in holographic entanglement entropy for strip sub-region in such gravity solutions up to third order and try to formulate a first law of entanglement thermodynamics including higher order corrections. The first law receives important contribution from an entanglement chemical potential in presence of boost. We find that suitable modifications to the entanglement temperature and entanglement chemical potential are required to account for higher order corrections. The results can be extended to non-conformal cases and AdS plane wave background.

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