On the duality condition for a Hermitian scalar field

Bisognano, J.J.; Wichmann, Eyvind H.

doi:10.1063/1.522605

Cited by 524 publications

(674 citation statements)

References 26 publications

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“…If, however, the unperturbed background is such that the undeformed entangling surface exhibits rotational symmetry in the transverse space, then this symmetry will be inherent in the path integral representation ofρ 0 . In particular, as shown in [23] (see also [37][38][39][40][41]) in this caseK 0 is identical to the generator of angular evolution around Σ andÛ takes the form…”

Section: Jhep12(2014)179mentioning

confidence: 76%

Entanglement entropy: a perturbative calculation

Rosenhaus

Smolkin

2014

J. High Energ. Phys.

104

192

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We provide a framework for a perturbative evaluation of the reduced density matrix. The method is based on a path integral in the analytically continued spacetime. It suggests an alternative to the holographic and 'standard' replica trick calculations of entanglement entropy. We implement this method within solvable field theory examples to evaluate leading order corrections induced by small perturbations in the geometry of the background and entangling surface. Our findings are in accord with Solodukhin's formula for the universal term of entanglement entropy for four dimensional CFTs.

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Section: Jhep12(2014)179mentioning

confidence: 76%

Entanglement entropy: a perturbative calculation

Rosenhaus

Smolkin

2014

J. High Energ. Phys.

104

192

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“…A salient result in algebraic QFT due to Bisognano-Wichmann [116,117] states that the modular Hamiltonian corresponding to this density matrix K Rindler is just the Minkowski boost generator in the direction X 1 . It implements a modular evolution as a Rindler time…”

Section: A Sequence Of Conformal Maps: Let Us Consider a Ball-shaped mentioning

confidence: 99%

Holographic Entanglement Entropy

Rangamani

Takayanagi

2017

Holographic Entanglement Entropy

115

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We review the developments in the past decade on holographic entanglement entropy, a subject that has garnered much attention owing to its potential to teach us about the emergence of spacetime in holography. We provide an introduction to the concept of entanglement entropy in quantum field theories, review the holographic proposals for computing the same, providing some justification for where these proposals arise from in the first two parts. The final part addresses recent developments linking entanglement and geometry. We provide an overview of the various arguments and technical developments that teach us how to use field theory entanglement to detect geometry. Our discussion is by design eclectic; we have chosen to focus on developments that appear to us most promising for further insights into the holographic map. This is a preliminary draft of a few chapters of a book which will appear sometime in the near future, to be published by Springer, as part of their Lecture Notes in Physics series. The book in addition contains a discussion of application of holographic ideas to computation of entanglement entropy in strongly coupled field theories, and discussion of tensor networks and holography, which we have chosen to exclude from the current manuscript. i AcknowledgmentsWe have been extremely fortunate to benefit from the wisdom and deep physical intuition of our wonderful collaborators Veronika Hubeny and Shinsei Ryu who played a pivotal role in helping us develop the basic picture relating quantum entanglement and holography. The importance of their role in shaping the story of holography entanglement entropy cannot be overstated.We have also enjoyed many excellent collaborations in our explorations over the past decade on this subject: thanks to

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“…This task is facilitated by the fact that in the models at hand, the modular data J, ∆ of (M, Ω) are known to act geometrically "correct", i.e. as expected from the Bisognano-Wichmann theorem [8,9]. More precisely, the modular conjugation coincides with the TCP operator, J = U (j) (3.33), and the modular unitaries are given by the boost transformations ∆ it = U (0, −2πt) [17].…”

Section: ) and (341) Satisfies The Assumptions A1)-a3) Of Sectionmentioning

confidence: 99%

Construction of Quantum Field Theories with Factorizing S-Matrices

Lechner¹

2007

Commun. Math. Phys.

122

405

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A new approach to the construction of interacting quantum field theories on two-dimensional Minkowski space is discussed. In this program, models are obtained from a prescribed factorizing S-matrix in two steps. At first, quantum fields which are localized in infinitely extended, wedge-shaped regions of Minkowski space are constructed explicitly. In the second step, local observables are analyzed with operator-algebraic techniques, in particular by using the modular nuclearity condition of Buchholz, d'Antoni and Longo.Besides a model-independent result regarding the Reeh-Schlieder property of the vacuum in this framework, an infinite class of quantum field theoretic models with non-trivial interaction is constructed. This construction completes a program initiated by Schroer in a large family of theories, a particular example being the Sinh-Gordon model. The crucial problem of establishing the existence of local observables in these models is solved by verifying the modular nuclearity condition, which here amounts to a condition on analytic properties of form factors of observables localized in wedge regions.It is shown that the constructed models solve the inverse scattering problem for the considered class of S-matrices. Moreover, a proof of asymptotic completeness is obtained by explicitly computing total sets of scattering states. The structure of these collision states is found to be in agreement with the heuristic formulae underlying the Zamolodchikov-Faddeev algebra.

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On the duality condition for a Hermitian scalar field

Cited by 524 publications

References 26 publications

Entanglement entropy: a perturbative calculation

Entanglement entropy: a perturbative calculation

Holographic Entanglement Entropy

Construction of Quantum Field Theories with Factorizing S-Matrices

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