Algebraic Holography

Rehren, Karl-Henning

doi:10.1007/pl00001009

Cited by 83 publications

(137 citation statements)

References 21 publications

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“…9 To express this in Rindler coordinates it is convenient to define the left and right Rindler boundary fields φ Rindler , L/R 0 (t) = lim r→∞ r ∆ φ(t, r) where L (R) refers to the left (right) Rindler wedge. Near the boundary…”

Section: Smearing Functionsmentioning

confidence: 99%

Local bulk operators in AdS/CFT correspondence: A boundary view of horizons and locality

et al. 2006

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We develop the representation of local bulk fields in AdS by non-local operators on the boundary, working in the semiclassical limit and using AdS 2 as our main example. In global coordinates we show that the boundary operator has support only at points which are spacelike separated from the bulk point. We construct boundary operators that represent local bulk operators inserted behind the horizon of the Poincaré patch and inside the Rindler horizon of a two dimensional black hole. We show that these operators respect bulk locality and comment on the generalization of our construction to higher dimensional AdS black holes.

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Section: Smearing Functionsmentioning

confidence: 99%

Local bulk operators in AdS/CFT correspondence: A boundary view of horizons and locality

et al. 2006

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“…The correspondence in the two dimensional case was studied in [9]. Results arisen by those works were proven rigorously by Rehren for free quantum fields in a AdS background, exstablishing the existence of a correspondence between bulk observables and boundary observables (usually called algebraic holography) without employing string technology [10,11]. Finally, Strominger [12] proposed to enlarge the found results by showing that there is an analogous correspondence between dS space and a possible conformal field theory on its timelike boundary.…”

Section: Introductionmentioning

confidence: 99%

Holography and SL(2,ℝ) symmetry in 2D Rindler space–time

Moretti

Pinamonti

2003

Journal of Mathematical Physics

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It is shown that it is possible to define quantum field theory of a massless scalar free field on the Killing horizon of a 2D-Rindler spacetime. Free quantum field theory on the horizon enjoys diffeomorphism invariance and turns out to be unitarily and algebraically equivalent to the analogous theory of a scalar field propagating inside Rindler spacetime, nomatter the value of the mass of the field in the bulk. More precisely, there exists a unitary transformation that realizes the bulk-boundary correspondence under an appropriate choice for Fock representation spaces. Secondly, the found correspondence is a subcase of an analogous algebraic correspondence described by injective * -homomorphisms of the abstract algebras of observables generated by abstract quantum free-field operators. These field operators are smeared with suitable test functions in the bulk and exact 1-forms on the horizon. In this sense the correspondence is independent from the chosen vacua. It is proven that, under that correspondence the "hidden" 1 SL(2, R) quantum symmetry found in a previous work gets a clear geometric meaning, it being associated with a group of diffeomorphisms of the horizon itself.2

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“…For the case at hand, starting from a physical AdS theory, one obtains an "overpopulated" CFT model which has its outing in the poltergeist phenomenon. In the opposite direction a "physical healthy" CFT passes to an "anemic" AdS theory, in which one has to look at noncompact regions in order to find any degrees of freedom [91].…”

Section: Localization and Phase-space Degrees Of Freedommentioning

confidence: 99%

Modular localization and the holistic structure of causal quantum theory, a historical perspective

Schroer

2014

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Recent insights into the conceptual structure of localization in QFT ("modular localization") led to clarifications of old unsolved problems. The oldest one is the Einstein-Jordan conundrum which led Jordan in 1925 to the discovery of quantum field theory. This comparison of fluctuations in subsystems of heat bath systems (Einstein) with those resulting from the restriction of the QFT vacuum state to an open subvolume (Jordan) leads to a perfect analogy; the globally pure vacuum state becomes upon local restriction a strongly impure KMS state. This phenomenon of localization-caused thermal behavior as well as the vacuum-polarization clouds at the causal boundary of the localization region places localization in QFT into a sharp contrast with quantum mechanics and justifies the attribute "holstic". In fact it positions the E-J Gedankenexperiment into the same conceptual category as the cosmological constant problem and the Unruh Gedankenexperiment. The holistic structure of QFT resulting from "modular localization" also leads to a revision of the conceptual origin of the crucial crossing property which entered particle theory at the time of the bootstrap S-matrix approach but suffered from incorrect use in the S-matrix settings of the dual model and string theory.The new holistic point of view, which strengthens the autonomous aspect of QFT, also comes with new messages for gauge theory by exposing the clash between Hilbert space structure and localization and presenting alternative solutions based on the use of stringlocal fields in Hilbert space. Among other things this leads to a radical reformulation of the Englert-Higgs symmetry breaking mechanism. Contents 1 Introduction 282 Vacuum polarization, area law 383 Modular localization and its thermal manifestation 424 The E-J conundrum, Jordan's model 545 Particle crossing, on-shell constructions from modular setting 58 PrefaceThe subject of this paper grew out of many discussions about Jordan's discovery of quantum field theory (QFT) which I had with the late Jürgen Ehlers. These conversations focussed in particular on events between the publication of Jordan's thesis on quantum aspects of statistical quantum mechanics in 1924 [1], and his discovery of QFT which was published in one section of the famous 1926 "Dreimännerarbeit" [2] together with Born and Heisenberg. This famous paper was in fact conceived as the second paper on quantum mechanics (QM). The resistance of Born and Heisenberg against Jordan's section has its natural explanation in that these two authors felt that Jordan was burdening the conceptual struggle to understand the new quantum mechanics with something which was even further out. I met Jürgen Ehlers the first time around 1957 at the University of Hamburg when he was Jordan's assistant and played the leading role in Jordan's general relativity seminar. Our paths split, after I wrote my diploma thesis on a topic of particle theory at the time when particle physics moved away from the university to the newly constructed high energy la...

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Algebraic Holography

Cited by 83 publications

References 21 publications

Local bulk operators in AdS/CFT correspondence: A boundary view of horizons and locality

Local bulk operators in AdS/CFT correspondence: A boundary view of horizons and locality

Holography and SL(2,ℝ) symmetry in 2D Rindler space–time

Modular localization and the holistic structure of causal quantum theory, a historical perspective

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