scholarly journals Spread of Entanglement in Non-Relativistic Theories

2018 ◽  
Vol 2018 ◽  
pp. 1-27
Author(s):  
Sagar F. Lokhande
Keyword(s):  
Broad Class ◽  
Entanglement Entropy ◽  
Time Dependent ◽  
Quantum Field Theories ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Instantaneous Power ◽  
Holographic Entanglement Entropy ◽  
Quantum Quenches ◽  
Good Order

We use a simple holographic toy model to study global quantum quenches in strongly coupled, hyperscaling-violating-Lifshitz quantum field theories using entanglement entropy as a probe. Generalizing our conformal field theory results, we show that the holographic entanglement entropy of small subsystems can be written as a simple linear response relation. We use this relation to derive a time-dependent first law of entanglement entropy. In general, this law has a time-dependent term resembling relative entropy which we propose as a good order parameter to characterize out-of-equilibrium states in the post-quench evolution. We use these tools to study a broad class of quantum quenches in detail: instantaneous, power law, and periodic.

Aspects of subregion holographic complexity

2019 ◽  
Vol 28 (15) ◽  
pp. 1930023 ◽  
Author(s):  
Davood Momeni ◽  
Nayereh Majd ◽  
Mudhahir Al Ajmi
Keyword(s):  
Review Paper ◽  
Entanglement Entropy ◽  
Time Dependent ◽  
Conformal Field ◽  
Cavalieri Principle ◽  
Holographic Superconductors ◽  
Holographic Entanglement Entropy ◽  
Ads Spacetime ◽  
General Deformation ◽  
Ads Geometry

This is a mini-review about the rapidly growing subject of dual holographic complexity (HC) for subsystems in conformal field theory (CFT) using a subregion volume enclosed by the entangled area in the dual bulk theory. This proposal is named as HC = volume. We use this proposal to compute the HC for different geometries in bulk theory. Because this HC quantity diverges as a result of the existence of the UV cutoff in the CFT, we proposed a suitable regularization scheme by subtracting the contribution of the background (pure) AdS spacetime from the deformation of the AdS geometry. Furthermore, the time-dependent geometries are investigated using the AdS/CFT proposal and hence, we proposed a time-dependent copy for HC in such nonstatic geometries. As an attempt to make a relation between HC and holographic entanglement entropy (HEE), inspired from the pure geometrical origins, we showed that HC and HEE which are duals to different volumes/areas in the bulk theory would be connected in a universal form for a general deformation AdS geometry (called holographic Cavalieri principle). As a pioneering idea we build a holographic model for [Formula: see text] critically in black holes via regularized HC as the dual thermodynamic volume. The second-order phase transitions in two-dimensional holographic superconductors is explained by using the regularized HC as an order parameter. All the results presented in this mini-review are collected from the list of published works of the first author of this paper. In several cases, we gave further explanation and clarification to make the ideas more understandable to the community. Other proposals for complexity like complexity as on shell action are not included in this review paper.

scholarly journals Chern-Simons gravity dual of BCFT

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Tadashi Takayanagi ◽  
Takahiro Uetoko
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Entanglement Entropy ◽  
Einstein Gravity ◽  
Conformal Field ◽  
Holographic Entanglement Entropy ◽  
The World ◽  
Higher Spin ◽  
End Of The World ◽  
Chern Simons

Abstract In this paper we provide a Chern-Simons gravity dual of a two dimensional conformal field theory on a manifold with boundaries, so called boundary conformal field theory (BCFT). We determine the correct boundary action on the end of the world brane in the Chern-Simons gauge theory. This reproduces known results of the AdS/BCFT for the Einstein gravity. We also give a prescription of calculating holographic entanglement entropy by employing Wilson lines which extend from the AdS boundary to the end of the world brane. We also discuss a higher spin extension of our formulation.

scholarly journals Holographic entanglement entropy for noncommutative anti-de Sitter space

2016 ◽  
Vol 31 (12) ◽  
pp. 1650073
Author(s):  
Davood Momeni ◽  
Muhammad Raza ◽  
Ratbay Myrzakulov
Keyword(s):  
Field Theory ◽  
Hilbert Space ◽  
Conformal Field Theory ◽  
Surface State ◽  
Central Charge ◽  
Entanglement Entropy ◽  
Quantum Effects ◽  
De Sitter ◽  
Conformal Field ◽  
Holographic Entanglement Entropy

A metric is proposed to explore the noncommutative form of the anti-de Sitter (AdS) space due to quantum effects. It has been proved that the noncommutativity in AdS space induces a single component gravitoelectric field. The holographic Ryu–Takayanagi (RT) algorithm is then applied to compute the entanglement entropy (EE) in dual CFT2. This calculation can be exploited to compute ultraviolet–infrared (UV–IR) cutoff dependent central charge of the certain noncommutative CFT2. This noncommutative computation of the EE can be interpreted in the form of the surface/state correspondence. We have shown that noncommutativity increases the dimension of the effective Hilbert space of the dual conformal field theory (CFT).

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.

COVARIANT ENTANGLEMENT ENTROPY

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2074-2081 ◽  
Author(s):  
TADASHI TAKAYANAGI
Keyword(s):  
Entanglement Entropy ◽  
Field Theories ◽  
Covariant Formulation ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Holographic Entanglement Entropy ◽  
Entropy Bound ◽  
Recent Formulation

We review our recent formulation1,2 of computing entanglement entropy in a holographic way. The basic examples can be found by applying AdS/CFT correspondence and the holographic formula has successfully been checked in many examples of conformal field theories. We also explain the covariant formulation of holographic entanglement entropy which is closely related to the covariant entropy bound (Bousso bound) in an interesting way.

scholarly journals Entanglement entropy inequalities in BCFT by holography

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Chia-Jui Chou ◽  
Bo-Han Lin ◽  
Bin Wang ◽  
Yi Yang
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Mutual Information ◽  
Entanglement Entropy ◽  
Conformal Field ◽  
Holographic Entanglement Entropy ◽  
Entropy Inequalities

Abstract We study entanglement entropy inequalities in boundary conformal field theory (BCFT) by holographic correspondence. By carefully classifying all the configurations for different phases, we prove the strong subadditiviy and the monogamy of mutual information for holographic entanglement entropy in BCFT at both zero and finite temperatures.

scholarly journals Surface defect, anomalies and b-extremization

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Yifan Wang
Keyword(s):  
Surface Defect ◽  
Surface Defects ◽  
Field Theories ◽  
Universal Relation ◽  
Quantum Field Theories ◽  
Conformal Field Theories ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Free Scalar ◽  
Monotonically Decrease

Abstract Quantum field theories (QFT) in the presence of defects exhibit new types of anomalies which play an important role in constraining the defect dynamics and defect renormalization group (RG) flows. Here we study surface defects and their anomalies in conformal field theories (CFT) of general spacetime dimensions. When the defect is conformal, it is characterized by a conformal b-anomaly analogous to the c-anomaly of 2d CFTs. The b-theorem states that b must monotonically decrease under defect RG flows and was proven by coupling to a spurious defect dilaton. We revisit the proof by deriving explicitly the dilaton effective action for defect RG flow in the free scalar theory. For conformal surface defects preserving $$ \mathcal{N} $$ N = (0, 2) supersymmetry, we prove a universal relation between the b-anomaly and the ’t Hooft anomaly for the U(1)r symmetry. We also establish the b-extremization principle that identifies the superconformal U(1)r symmetry from $$ \mathcal{N} $$ N = (0, 2) preserving RG flows. Together they provide a powerful tool to extract the b-anomaly of strongly coupled surface defects. To illustrate our method, we determine the b-anomalies for a number of surface defects in 3d, 4d and 6d SCFTs. We also comment on manifestations of these defect conformal and ’t Hooft anomalies in defect correlation functions.

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