scholarly journals Physical generalizations of the Rényi entropy

2019 ◽  
Vol 28 (07) ◽  
pp. 1950091 ◽  
Author(s):  
Clifford V. Johnson
Keyword(s):  
Field Theory ◽  
Thermodynamic Quantity ◽  
Natural Generalization ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
De Sitter ◽  
Information Theoretic ◽  
Conformal Field ◽  
Sitter Spacetime ◽  
Twist Operators

We present a new type of generalization of the Rényi entropy that follows naturally from its representation as a thermodynamic quantity. We apply it to the case of [Formula: see text]-dimensional conformal field theories (CFTs) reduced on a region bounded by a sphere. It is known how to compute their Rényi entropy as an integral of the thermal entropy of hyperbolic black holes in [Formula: see text]-dimensional anti-de Sitter spacetime. We show how this integral fits into the framework of extended gravitational thermodynamics, and then point out the natural generalization of the Rényi entropy that suggests itself in that light. In the field theory terms, the new generalization employs aspects of the physics of Renormalization Group (RG) flow to define a refined version of the reduced vacuum density matrix. For [Formula: see text], it can be derived directly in terms of twist operators in field theory. The framework presented here may have applications beyond this context, perhaps in studies of both quantum and classical information theoretic properties of a variety of systems.

scholarly journals Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part II. Multi-particle states

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Jiaju Zhang ◽  
M. A. Rajabpour
Keyword(s):  
Field Theory ◽  
Excited State ◽  
Excited States ◽  
Short Interval ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Two Dimensional ◽  
Bosonic Field ◽  
Conformal Field ◽  
Harmonic Chain

Abstract We study the excited state Rényi entropy and subsystem Schatten distance in the two-dimensional free massless non-compact bosonic field theory, which is a conformal field theory. The discretization of the free non-compact bosonic theory gives the harmonic chain with local couplings. We consider the field theory excited states that correspond to the harmonic chain states with excitations of more than one quasiparticle, which we call multi-particle states. This extends the previous work by the same authors to more general excited states. In the field theory we obtain the exact Rényi entropy and subsystem Schatten distance for several low-lying states. We obtain short interval expansion of the Rényi entropy and subsystem Schatten distance for general excited states, which display different universal scaling behaviors in the gapless and extremely gapped limits of the non-compact bosonic theory. In the locally coupled harmonic chain we calculate numerically the excited state Rényi entropy and subsystem Schatten distance using the wave function method. We find excellent matches of the analytical results in the field theory and numerical results in the gapless limit of the harmonic chain. We also make some preliminary investigations of the Rényi entropy and the subsystem Schatten distance in the extremely gapped limit of the harmonic chain.

scholarly journals BMS symmetry via AdS/CFT

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
David A. Lowe ◽  
David M. Ramirez
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Three Dimensional ◽  
Virasoro Algebra ◽  
Radius Of Curvature ◽  
Large Radius ◽  
De Sitter ◽  
Natural Action ◽  
Conformal Field ◽  
Sitter Spacetime

Abstract With a view to understanding extended-BMS symmetries in the framework of the AdS4/CFT3 correspondence, asymptotically AdS geometries are constructed with null impulsive shockwaves involving a discontinuity in superrotation parameters. The holographic dual is proposed to be a two-dimensional Euclidean defect conformal field localized on a particular timeslice in a three-dimensional conformal field theory on de Sitter spacetime. The defect conformal field theory generates a natural action of the Virasoro algebra. The large radius of curvature limit ℓ → ∞ yields spacetimes with nontrivial extended-BMS charges corresponding to a single set of Virasoro charges.

scholarly journals Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part I. Single-particle states

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jiaju Zhang ◽  
M.A. Rajabpour
Keyword(s):  
Excited States ◽  
Single Particle ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Large Momentum ◽  
Particle State ◽  
Two Dimensional ◽  
Universal Form ◽  
Conformal Field ◽  
Harmonic Chain

Abstract We investigate the Rényi entropy of the excited states produced by the current and its derivatives in the two-dimensional free massless non-compact bosonic theory, which is a two-dimensional conformal field theory. We also study the subsystem Schatten distance between these states. The two-dimensional free massless non-compact bosonic theory is the continuum limit of the finite periodic gapless harmonic chains with the local interactions. We identify the excited states produced by current and its derivatives in the massless bosonic theory as the single-particle excited states in the gapless harmonic chain. We calculate analytically the second Rényi entropy and the second Schatten distance in the massless bosonic theory. We then use the wave functions of the excited states and calculate the second Rényi entropy and the second Schatten distance in the gapless limit of the harmonic chain, which match perfectly with the analytical results in the massless bosonic theory. We verify that in the large momentum limit the single-particle state Rényi entropy takes a universal form. We also show that in the limit of large momenta and large momentum difference the subsystem Schatten distance takes a universal form but it is replaced by a new corrected form when the momentum difference is small. Finally we also comment on the mutual Rényi entropy of two disjoint intervals in the excited states of the two-dimensional free non-compact bosonic theory.

scholarly journals ANTI-DE-SITTER SPACE, BRANES, SINGLETONS, SUPERCONFORMAL FIELD THEORIES AND ALL THAT

1999 ◽  
Vol 14 (06) ◽  
pp. 815-843 ◽  
Author(s):  
M. J. DUFF
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Historical Review ◽  
De Sitter Space ◽  
Field Theories ◽  
De Sitter ◽  
Superconformal Field Theories ◽  
Conformal Field ◽  
New Approaches ◽  
The Universe

There has recently been a revival of interest in anti-de-Sitter space (AdS), brought about by the conjectured duality between physics in the bulk of AdS and a conformal field theory on the boundary. Since the whole subject of branes, singletons and superconformal field theories on the AdS boundary was an active area of research about ten years ago, we begin with a historical review, including the idea of the "membrane at the end of the universe." We then compare the old and new approaches and discuss some new results on AdS 5 × S5 and AdS 3 × S3.

scholarly journals SUPERGRAVITY DESCRIPTION OF FIELD THEORIES ON CURVED MANIFOLDS AND A NO GO THEOREM

2001 ◽  
Vol 16 (05) ◽  
pp. 822-855 ◽  
Author(s):  
JUAN MALDACENA ◽  
CARLOS NUÑEZ
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Riemann Surface ◽  
Riemann Surfaces ◽  
Field Theories ◽  
De Sitter ◽  
Curved Manifolds ◽  
Conformal Field ◽  
Low Energies ◽  
M Theory

In the first part of this paper we find supergravity solutions corresponding to branes on worldvolumes of the form Rd×Σ where Σ is a Riemann surface. These theories arise when we wrap branes on holomorphic Riemann surfaces inside K3 or CY manifolds. In some cases the theory at low energies is a conformal field theory with two less dimensions. We find some non-singular supersymmetric compactifications of M-theory down to AdS5. We also propose a criterion for permissible singularities in supergravity solutions. In the second part of this paper, which can be read independently of the first, we show that there are no non-singular Randall-Sundrum or de-Sitter compactifications for large class of gravity theories.

scholarly journals AdS3 GRAVITATIONAL INSTANTONS FROM CONFORMAL FIELD THEORY

1999 ◽  
Vol 14 (28) ◽  
pp. 1961-1981 ◽  
Author(s):  
SHUHEI MANO
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Bound States ◽  
Three Dimensional ◽  
Partition Functions ◽  
De Sitter ◽  
Btz Black Hole ◽  
Gravitational Instantons ◽  
Conformal Field ◽  
Horizon Geometry

A conformal field theory on the boundary of three-dimensional asymptotic anti-de Sitter spaces which appear as near horizon geometry of D-brane bound states is discussed. It is shown that partition functions of gravitational instantons appear as high and low temperature limits of the partition function of the conformal field theory. The result reproduces phase transition between the anti-de Sitter space and the BTZ black hole in the bulk gravity.

scholarly journals Shannon, Rényi, Tsallis Entropies and Onicescu Information Energy for Low-Lying Singly Excited States of Helium

Atoms ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 70 ◽  
Author(s):  
Jen-Hao Ou ◽  
Yew Kam Ho
Keyword(s):  
Excited States ◽  
Shannon Entropy ◽  
Electronic Structures ◽  
Tsallis Entropy ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Electron Delocalization ◽  
Information Theoretic ◽  
Molecular Systems ◽  
Information Energy

Knowledge of the electronic structures of atomic and molecular systems deepens our understanding of the desired system. In particular, several information-theoretic quantities, such as Shannon entropy, have been applied to quantify the extent of electron delocalization for the ground state of various systems. To explore excited states, we calculated Shannon entropy and two of its one-parameter generalizations, Rényi entropy of order α and Tsallis entropy of order α , and Onicescu Information Energy of order α for four low-lying singly excited states (1s2s 1 S e , 1s2s 3 S e , 1s3s 1 S e , and 1s3s 3 S e states) of helium. This paper compares the behavior of these three quantities of order 0.5 to 9 for the ground and four excited states. We found that, generally, a higher excited state had a larger Rényi entropy, larger Tsallis entropy, and smaller Onicescu information energy. However, this trend was not definite and the singlet–triplet reversal occurred for Rényi entropy, Tsallis entropy and Onicescu information energy at a certain range of order α .

scholarly journals Advances in String Theory in Curved Backgrounds: A Synthesis Report

2003 ◽  
Vol 18 (12) ◽  
pp. 2011-2022 ◽  
Author(s):  
N. G. Sanchez
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
String Theory ◽  
Quantum Field ◽  
De Sitter ◽  
Conformal Field ◽  
Dual Relation ◽  
New Feature ◽  
Synthesis Report ◽  
Gravitational Wave Background

A synthetic report of the advances in the study of classical and quantum string dynamics in curved backgrounds is provided, namely : the new feature of Multistring solutions; the mass spectrum of Strings in Curved backgrounds; The effect of a Cosmological Constant and of Spacial Curvature on Classical and Quantum Strings; Classical splitting of Fundamental Strings; The General String Evolution in constant Curvature Spacetimes; The Conformal Invariance Effects; Strings on plane fronted and gravitational shock waves, string falling on spacetime singularities and its spectrum. New Developments in String Gravity and String Cosmology are reported: String driven cosmology and its Predictions; The primordial gravitational wave background; Non-singular string cosmologies from Exact Conformal Field Theories; Quantum Field Theory, String Temperature and the String Phase of de Sitter space-time; Hawking Radiation in String Theory and the String Phase of Black Holes; New Dual Relation between Quantum Field Theory regime and String regime and the "QFT/String Tango"; New Coherent String States and Minimal Uncertainty Principle in string theory.

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