Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, p-forms

Abstract We show that the entanglement entropy of D = 4 linearized gravitons across a sphere recently computed by Benedetti and Casini coincides with that obtained using the Kaluza-Klein tower of traceless transverse massive spin-2 fields on S1× AdS3. The mass of the constant mode on S1 saturates the Brietenholer-Freedman bound in AdS3. This condition also ensures that the entanglement entropy of higher spins determined from partition functions on the hyperbolic cylinder coincides with their recent conjecture. Starting from the action of the 2-form on S1× AdS5 and fixing gauge, we evaluate the entanglement entropy across a sphere as well as the dimensions of the corresponding twist operator. We demonstrate that the conformal dimensions of the corresponding twist operator agrees with that obtained using the expectation value of the stress tensor on the replica cone. For conformal p-forms in even dimensions it obeys the expected relations with the coefficients determining the 3-point function of the stress tensor of these fields.

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Defect CFT techniques in the 6d $$ \mathcal{N} $$ = (2, 0) theory

Journal of High Energy Physics ◽

10.1007/jhep03(2021)261 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Nadav Drukker ◽

Malte Probst ◽

Maxime Trépanier

Keyword(s):

Stress Tensor ◽

Unitary Representations ◽

Point Function ◽

Displacement Operator ◽

Expectation Value ◽

Operator Expansion ◽

Bulk Stress ◽

Defect Operator ◽

Tensor Multiplet

Abstract Surface operators are among the most important observables of the 6d $$ \mathcal{N} $$ N = (2, 0) theory. Here we apply the tools of defect CFT to study local operator insertions into the 1/2-BPS plane. We first relate the 2-point function of the displacement operator to the expectation value of the bulk stress tensor and translate this relation into a constraint on the anomaly coefficients associated with the defect. Secondly, we study the defect operator expansion of the stress tensor multiplet and identify several new operators of the defect CFT. Technical results derived along the way include the explicit supersymmetry tranformations of the stress tensor multiplet and the classification of unitary representations of the superconformal algebra preserved by the defect.

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Partition functions of p-forms from Harish-Chandra characters

Journal of High Energy Physics ◽

10.1007/jhep09(2021)094 ◽

2021 ◽

Vol 2021 (9) ◽

Author(s):

Justin R. David ◽

Jyotirmoy Mukherjee

Keyword(s):

Free Energy ◽

Partition Function ◽

Integral Representation ◽

Integral Transform ◽

Entanglement Entropy ◽

Integral Transforms ◽

Partition Functions ◽

De Sitter ◽

Symmetric Tensors ◽

Hyperbolic Cylinders

Abstract We show that the determinant of the co-exact p-form on spheres and anti-de Sitter spaces can be written as an integral transform of bulk and edge Harish-Chandra characters. The edge character of a co-exact p-form contains characters of anti-symmetric tensors of rank lower to p all the way to the zero-form. Using this result we evaluate the partition function of p-forms and demonstrate that they obey known properties under Hodge duality. We show that the partition function of conformal forms in even d + 1 dimensions, on hyperbolic cylinders can be written as integral transforms involving only the bulk characters. This supports earlier observations that entanglement entropy evaluated using partition functions on hyperbolic cylinders do not contain contributions from the edge modes. For conformal coupled scalars we demonstrate that the character integral representation of the free energy on hyperbolic cylinders and branched spheres coincide. Finally we propose a character integral representation for the partition function of p-forms on branched spheres.

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The 3d $$ \mathcal{N} $$ = 6 bootstrap: from higher spins to strings to membranes

Journal of High Energy Physics ◽

10.1007/jhep05(2021)083 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Damon J. Binder ◽

Shai M. Chester ◽

Max Jerdee ◽

Silviu S. Pufu

Keyword(s):

Block Decomposition ◽

Point Function ◽

Present Evidence ◽

Bootstrap Techniques ◽

Wide Range ◽

Higher Spin ◽

Tensor Multiplet ◽

Higher Spins ◽

M Theory ◽

Chern Simons

Abstract We study the space of 3d $$ \mathcal{N} $$ N = 6 SCFTs by combining numerical bootstrap techniques with exact results derived using supersymmetric localization. First we derive the superconformal block decomposition of the four-point function of the stress tensor multiplet superconformal primary. We then use supersymmetric localization results for the $$ \mathcal{N} $$ N = 6 U(N)k × U(N + M)−k Chern-Simons-matter theories to determine two protected OPE coefficients for many values of N, M, k. These two exact inputs are combined with the numerical bootstrap to compute precise rigorous islands for a wide range of N, k at M = 0, so that we can non-perturbatively interpolate between SCFTs with M-theory duals at small k and string theory duals at large k. We also present evidence that the localization results for the U(1)2M × U (1 + M)−2M theory, which has a vector-like large-M limit dual to higher spin theory, saturates the bootstrap bounds for certain protected CFT data. The extremal functional allows us to then conjecturally reconstruct low-lying CFT data for this theory.

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Unitarity in KK-graviton production, a case study in warped extra-dimensions

Journal of High Energy Physics ◽

10.1007/jhep04(2021)143 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

A. de Giorgi ◽

S. Vogl

Keyword(s):

Extra Dimensions ◽

Sum Rules ◽

Effective Theory ◽

Higher Dimensional ◽

Massive Spin ◽

The Matrix ◽

Dimensional Gravity ◽

Warped Extra Dimensions ◽

Kaluza Klein

Abstract The Kaluza-Klein (KK) decomposition of higher-dimensional gravity gives rise to a tower of KK-gravitons in the effective four-dimensional (4D) theory. Such massive spin-2 fields are known to be connected with unitarity issues and easily lead to a breakdown of the effective theory well below the naive scale of the interaction. However, the breakdown of the effective 4D theory is expected to be controlled by the parameters of the 5D theory. Working in a simplified Randall-Sundrum model we study the matrix elements for matter annihilations into massive gravitons. We find that truncating the KK-tower leads to an early breakdown of perturbative unitarity. However, by considering the full tower we obtain a set of sum rules for the couplings between the different KK-fields that restore unitarity up to the scale of the 5D theory. We prove analytically that these are fulfilled in the model under consideration and present numerical tests of their convergence. This work complements earlier studies that focused on graviton self-interactions and yields additional sum rules that are required if matter fields are incorporated into warped extra-dimensions.

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Entanglement entropy for $$ \mathrm{T}\overline{\mathrm{T}} $$, $$ \mathrm{J}\overline{\mathrm{T}} $$, $$ \mathrm{T}\overline{\mathrm{J}} $$ deformed holographic CFT

Journal of High Energy Physics ◽

10.1007/jhep02(2021)096 ◽

2021 ◽

Vol 2021 (2) ◽

Author(s):

Soumangsu Chakraborty ◽

Akikazu Hashimoto

Keyword(s):

Parameter Space ◽

Wilson Loop ◽

Lorentz Invariance ◽

Entanglement Entropy ◽

Geodesic Equation ◽

Leading Order ◽

Theoretic Analysis ◽

Expectation Value ◽

Spatial Coordinates ◽

Single Trace

Abstract We derive the geodesic equation for determining the Ryu-Takayanagi surface in AdS3 deformed by single trace $$ \mu T\overline{T} $$ μT T ¯ + $$ {\varepsilon}_{+}J\overline{T} $$ ε + J T ¯ + $$ {\varepsilon}_{-}T\overline{J} $$ ε − T J ¯ deformation for generic values of (μ, ε+, ε−) for which the background is free of singularities. For generic values of ε±, Lorentz invariance is broken, and the Ryu-Takayanagi surface embeds non-trivially in time as well as spatial coordinates. We solve the geodesic equation and characterize the UV and IR behavior of the entanglement entropy and the Casini-Huerta c-function. We comment on various features of these observables in the (μ, ε+, ε−) parameter space. We discuss the matching at leading order in small (μ, ε+, ε−) expansion of the entanglement entropy between the single trace deformed holographic system and a class of double trace deformed theories where a strictly field theoretic analysis is possible. We also comment on expectation value of a large rectangular Wilson loop-like observable.

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Mixed scalar-current bootstrap in three dimensions

Journal of High Energy Physics ◽

10.1007/jhep12(2020)156 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Marten Reehorst ◽

Emilio Trevisani ◽

Alessandro Vichi

Keyword(s):

Stress Tensor ◽

Quantum Monte Carlo ◽

Three Dimensions ◽

Mixed System ◽

Point Function ◽

Function Coefficient ◽

Rigorous Bounds ◽

Usual Scalar ◽

Scalar Singlet ◽

Scalar Current

Abstract We study the mixed system of correlation functions involving a scalar field charged under a global U(1) symmetry and the associated conserved spin-1 current Jμ. Using numerical bootstrap techniques we obtain bounds on new observables not accessible in the usual scalar bootstrap. We then specialize to the O(2) model and extract rigorous bounds on the three-point function coefficient of two currents and the unique relevant scalar singlet, as well as those of two currents and the stress tensor. Using these results, and comparing with a quantum Monte Carlo simulation of the O(2) model conductivity, we give estimates of the thermal one-point function of the relevant singlet and the stress tensor. We also obtain new bounds on operators in various sectors.

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Functional Solution Scheme for Relativistic Strong Coupling Theor

Zeitschrift für Naturforschung A ◽

10.1515/zna-1964-7-802 ◽

1964 ◽

Vol 19 (7-8) ◽

pp. 828-834

Author(s):

G. Heber ◽

H. J. Kaiser

Keyword(s):

Vacuum Expectation ◽

Vacuum Expectation Value ◽

Functional Integral ◽

The Self ◽

Matrix Elements ◽

Point Function ◽

Expectation Value ◽

Lattice Space ◽

S Matrix ◽

Functional Solution

The vacuum expectation value of the S-matrix is represented, following HORI, as a functional integral and separated according to Svac=exp( — i W) ∫ D φ exp( —i ∫ dx Lw). Now, the functional integral involves only the part Lw of the Lagrangian without derivatives and can be easily calculated in lattice space. We propose a graphical scheme which formalizes the action of the operator W = f dx dy δ (x—y) (δ/δ(y))⬜x(δ/δ(x)) . The scheme is worked out in some detail for the calculation of the two-point-function of neutral BOSE fields with the self-interaction λ φM for even M. A method is proposed which under certain convergence assumptions should yield in a finite number of steps the lowest mass eigenvalues and the related matrix elements. The method exhibits characteristic differences between renormalizable and nonrenormalizable theories.

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Kerr-Newman stress-tensor from minimal coupling

Journal of High Energy Physics ◽

10.1007/jhep12(2020)103 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Ming-Zhi Chung ◽

Yu-tin Huang ◽

Jung-Wook Kim

Keyword(s):

Form Factor ◽

Stress Tensor ◽

Energy Tensor ◽

Stress Energy Tensor ◽

Minimal Coupling ◽

Massive Spin ◽

Stress Energy ◽

Newman Black Hole ◽

Higher Spin ◽

The One

Abstract In this paper, we demonstrate that at leading order in post Minkowskian (PM) expansion, the stress-energy tensor of Kerr-Newman black hole can be recovered to all orders in spin from three sets of minimal coupling: the electric and gravitational minimal coupling for higher-spin particles, and the “minimal coupling” for massive spin-2 decay. These couplings are uniquely defined from kinematic consideration alone. This is shown by extracting the classical piece of the one-loop stress-energy tensor form factor, which we provide a basis that is valid to all orders in spin. The 1 PM stress tensor, and the metric in the harmonic gauge, is then recovered from the classical spin limit of the form factor.

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