Quantum correction of the Wilson line and entanglement entropy in the pure AdS3 Einstein gravity theory

Abstract We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

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Chern-Simons gravity dual of BCFT

Journal of High Energy Physics ◽

10.1007/jhep04(2021)193 ◽

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.

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Holographic entanglement entropy of the Coulomb branch

Journal of High Energy Physics ◽

10.1007/jhep04(2021)153 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Adam Chalabi ◽

S. Prem Kumar ◽

Andy O’Bannon ◽

Anton Pribytok ◽

Ronnie Rodgers ◽

...

Keyword(s):

W Boson ◽

Wilson Line ◽

Entanglement Entropy ◽

Physical Principle ◽

Boson Mass ◽

Extremal Black Hole ◽

Energy Tensor ◽

Large Radius ◽

Coulomb Branch ◽

Yang Mills

Abstract We compute entanglement entropy (EE) of a spherical region in (3 + 1)-dimensional $$ \mathcal{N} $$ N = 4 supersymmetric SU(N) Yang-Mills theory in states described holographically by probe D3-branes in AdS5 × S5. We do so by generalising methods for computing EE from a probe brane action without having to determine the probe’s backreaction. On the Coulomb branch with SU(N) broken to SU(N − 1) × U(1), we find the EE monotonically decreases as the sphere’s radius increases, consistent with the a-theorem. The EE of a symmetric-representation Wilson line screened in SU(N − 1) also monotonically decreases, although no known physical principle requires this. A spherical soliton separating SU(N) inside from SU(N − 1) × U(1) outside had been proposed to model an extremal black hole. However, we find the EE of a sphere at the soliton’s radius does not scale with the surface area. For both the screened Wilson line and soliton, the EE at large radius is described by a position-dependent W-boson mass as a short-distance cutoff. Our holographic results for EE and one-point functions of the Lagrangian and stress-energy tensor show that at large distance the soliton looks like a Wilson line in a direct product of fundamental representations.

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NONRENORMALIZABILITY MAY BE SUPERFICIAL IN THE COVARIANT FORMALISM OF QUANTUM GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732395001629 ◽

1995 ◽

Vol 10 (21) ◽

pp. 1501-1506 ◽

Cited By ~ 2

Author(s):

MITSUO ABE ◽

NOBORU NAKANISHI

Keyword(s):

Perturbation Theory ◽

Quantum Gravity ◽

Ad Hoc ◽

Einstein Gravity ◽

Gravity Theory ◽

Usual Sense ◽

Covariant Formalism ◽

Perturbative Approach

It is pointed out that the nonrenormalizability of quantum Einstein gravity may be caused by the inadequacy of the conventional perturbative approach. It is more reasonable to reconsider the problem in the light of a newly proposed perturbative scheme, which is free of the ad hoc assumption on which the conventional perturbation theory is based. It is explicitly shown that there is a gravity-theory example which is nonrenormalizable in the usual sense but completely finite if the new perturbative scheme is applied.

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CONSTRAINTS ON SCALAR-TENSOR COSMOLOGY FROM WMAP DATA

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194511000250 ◽

2011 ◽

Vol 01 ◽

pp. 183-188 ◽

Cited By ~ 2

Author(s):

RYO NAGATA

Keyword(s):

Angular Spectrum ◽

Quadratic Extension ◽

Einstein Gravity ◽

Gravity Theory ◽

Observational Constraints ◽

Scalar Tensor Theory ◽

Tensor Theory ◽

Wmap Data

We place observational constraints on a scalar-tensor gravity theory by comparing the WMAP temperature and polarization angular spectrum with its predictions. We examined the quadratic extension of Brans-Dicke theory and found that, even if the scalar-tensor theory was far from Einstein gravity in early cosmological epochs, CMB can set stringent constraints on the deviations from Einstein gravity.

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A Second Law for higher curvature gravity

International Journal of Modern Physics D ◽

10.1142/s0218271815440149 ◽

2015 ◽

Vol 24 (12) ◽

pp. 1544014 ◽

Cited By ~ 26

Author(s):

Aron C. Wall

Keyword(s):

Black Holes ◽

Black Hole ◽

Quantum Gravity ◽

Entanglement Entropy ◽

Black Hole Thermodynamics ◽

Gravity Theory ◽

Second Law ◽

Holographic Entanglement Entropy ◽

Higher Curvature Gravity ◽

Complete Quantum

The Second Law of black hole thermodynamics is shown to hold for arbitrarily complicated theories of higher curvature gravity, so long as we allow only linearized perturbations to stationary black holes. Some ambiguities in Wald’s Noether charge method are resolved. The increasing quantity turns out to be the same as the holographic entanglement entropy calculated by Dong. It is suggested that only the linearization of the higher curvature Second Law is important, when consistently truncating a UV-complete quantum gravity theory.

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Holographic entanglement entropy for perturbative higher-curvature gravities

Journal of High Energy Physics ◽

10.1007/jhep04(2021)145 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Pablo Bueno ◽

Joan Camps ◽

Alejandro Vilar López

Keyword(s):

Functional Dependence ◽

Entanglement Entropy ◽

Einstein Gravity ◽

Universal Function ◽

Riemann Tensor ◽

Opening Angle ◽

Weighted Sum ◽

Holographic Entanglement Entropy ◽

Entropy Functional ◽

Quadratic Order

Abstract The holographic entanglement entropy functional for higher-curvature gravities involves a weighted sum whose evaluation, beyond quadratic order, requires a complicated theory-dependent splitting of the Riemann tensor components. Using the splittings of general relativity one can obtain unambiguous formulas perturbatively valid for general higher-curvature gravities. Within this setup, we perform a novel rewriting of the functional which gets rid of the weighted sum. The formula is particularly neat for general cubic and quartic theories, and we use it to explicitly evaluate the corresponding functionals. In the case of Lovelock theories, we find that the anomaly term can be written in terms of the exponential of a differential operator. We also show that order-n densities involving nR Riemann tensors (combined with n−nR Ricci’s) give rise to terms with up to 2nR− 2 extrinsic curvatures. In particular, densities built from arbitrary Ricci curvatures combined with zero or one Riemann tensors have no anomaly term in their functionals. Finally, we apply our results for cubic gravities to the evaluation of universal terms coming from various symmetric regions in general dimensions. In particular, we show that the universal function characteristic of corner regions in d = 3 gets modified in its functional dependence on the opening angle with respect to the Einstein gravity result.

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Entanglement entropy, scale-dependent dimensions and the origin of gravity

International Journal of Modern Physics D ◽

10.1142/s0218271817430301 ◽

2017 ◽

Vol 26 (12) ◽

pp. 1743030 ◽

Cited By ~ 2

Author(s):

Michele Arzano ◽

Gianluca Calcagni

Keyword(s):

Quantum Gravity ◽

Degrees Of Freedom ◽

Entanglement Entropy ◽

Boundary Surface ◽

Gravitational Theory ◽

Einstein Gravity ◽

Entropy Density ◽

Spectral Dimension ◽

Quantum Geometry

We argue that the requirement of a finite entanglement entropy of quantum degrees of freedom across a boundary surface is closely related to the phenomenon of running spectral dimension, universal in approaches to quantum gravity. If quantum geometry hinders diffusion, for instance, when its structure at some given scale is discrete or too rough, then the spectral dimension of spacetime vanishes at that scale and the entropy density blows up. A finite entanglement entropy is a key ingredient in deriving Einstein gravity in a semi-classical regime of a quantum-gravitational theory and, thus, our arguments strengthen the role of running dimensionality as an imprint of quantum geometry with potentially observable consequences.

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Nonvanishing finite scalar mass in flux compactification

Journal of High Energy Physics ◽

10.1007/jhep06(2021)159 ◽

2021 ◽

Vol 2021 (6) ◽

Author(s):

Takuya Hirose ◽

Nobuhito Maru

Keyword(s):

Effective Potential ◽

Quantum Correction ◽

Wilson Line ◽

Point Interaction ◽

Potential Analysis ◽

Flux Compactification ◽

Interaction Terms ◽

Scalar Mass

Abstract We study possibilities to realize a nonvanishing finite Wilson line (WL) scalar mass in flux compactification. Generalizing loop integrals in the quantum correction to WL mass at one-loop, we derive the conditions for the loop integrals and mode sums in one-loop corrections to WL scalar mass to be finite. We further guess and classify the four-point and three-point interaction terms satisfying these conditions. As an illustration, the nonvanishing finite WL scalar mass is explicitly shown in a six dimensional scalar QED by diagrammatic computation and effective potential analysis. This is the first example of finite WL scalar mass in flux compactification.

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More on Wilson toroidal networks and torus blocks

Journal of High Energy Physics ◽

10.1007/jhep11(2020)121 ◽

2020 ◽

Vol 2020 (11) ◽

Author(s):

Konstantin Alkalaev ◽

Vladimir Belavin

Keyword(s):

Boundary Conditions ◽

Wilson Line ◽

Tensor Products ◽

Symmetric Tensor ◽

Gravity Theory ◽

Matrix Elements ◽

Conformal Blocks ◽

Finite Dimensional ◽

The One ◽

Chern Simons

Abstract We consider the Wilson line networks of the Chern-Simons 3d gravity theory with toroidal boundary conditions which calculate global conformal blocks of degenerate quasi-primary operators in torus 2d CFT. After general discussion that summarizes and further extends results known in the literature we explicitly obtain the one-point torus block and two-point torus blocks through particular matrix elements of toroidal Wilson network operators in irreducible finite-dimensional representations of sl(2, ℝ) algebra. The resulting expressions are given in two alternative forms using different ways to treat multiple tensor products of sl(2, ℝ) representations: (1) 3mj Wigner symbols and intertwiners of higher valence, (2) totally symmetric tensor products of the fundamental sl(2, ℝ) representation.

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