Looking Beyond the Thermal Horizon: Hidden Symmetries in Chiral Models

Schroer, Bert; Wiesbrock, Hans‐Werner

doi:10.1142/s0129055x00000162

Cited by 23 publications

(51 citation statements)

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“…In that paper we show that, in fact, a suitable and natural enlargement in the Fock space of the hidden SL ( Essentially speaking, this is due to the behavior of n-point functions on the Killing horizon which is not Hadamard. In this context it would be interesting to investigate the holographic meaning of the Hadamard states (Minkowski vacuum and Hartle-Hawking state) also to make contact with results found in [15,16,17,18] where the net of Von Neumann algebras are defined with respect to Hadamard states.…”

Section: Sl(2 R) Unitary Representations On the Horizon Consider Qfmentioning

confidence: 88%

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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Section: Sl(2 R) Unitary Representations On the Horizon Consider Qfmentioning

confidence: 88%

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

Moretti

Pinamonti

2003

Journal of Mathematical Physics

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“…fluctuations in a small subinterval of a chiral QFT restricted to a halfline, is isomorphic to Einstein's Gedankenexperiment of thermal fluctuations in a heat bath thermodynamic limit state on a line restricted to an interval. Such a tight relation, also referred to a an inverse Unruh effect [24], can not be expected in higher spacetime dimension. Although the thermal aspect of a restricted vacuum in QFT is a structural consequence of causal localization, the general identification of the dimensionless modular temperature with an actual temperature of a heat bath system, or, which is equivalent, the modular "time" with the physical time is not correct; the modular Hamiltonian is does not describe the inertial time for which the local temperature defined in terms of the zeroth thermodynamic law agrees with the "Carnot temperature" of the second law [48].…”

Section: Theorem 1 ([24])mentioning

confidence: 99%

“…In fact in the special case of Jordan's chiral current model (the historically first and simplest model of a QFT), the solution of the E-J conundrum amounts to a unitary isomorphism between a system defined by the vacuum state restricted to the algebra A(I) localized in an interval I and an associated global statistical mechanics system at finite temperature. Such isomorphic relations are referred to as describing an "inverse Unruh effect", [24] and the Jordan model is the only known illustration. However in both cases the KMS temperature is not something which one can measure with a thermometer or use for "eggboiling" 6 (and there is also no "boiling soup" of particle/anti-particle pairs) since the acceleration only affects the "Carnot-temperature" [48].…”

Section: A(r) = B(h(r)) a ≡ B(h) = A(r) ⊗ A(r ⊥ )mentioning

confidence: 99%

“…For Jordan's chiral current model used in the E-J conundrum, the entropy can be directly obtained from the isometry with a chiral statistical mechanics model (section 4). This situation is very special and has been termed "the inverse Unruh effect [24]. For d=1+3 't Hooft has obtaind the area behavior in terms of the "brickwall picture" [32], but a rigorous derivation, solely based in the split property of modular localization, is not yet available.…”

Section: Vacuum Polarization Area Lawmentioning

confidence: 99%

“…There exists a conjecture that even in the general case there could be a weak form of the "inverse Unruh effect" [24] in which the spatial volume factor is replaced by the "volume factor" if a box with two spacelike and one lightlike direction. In that case the two spacelike extensions would account for the dimensionless area factor and the lightlike contribution would be (as in the chiral Jordan model) logarithmic [47] so that the net result is a logarithmically modified area law.…”

Section: Vacuum Polarization Area Lawmentioning

confidence: 99%

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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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Modular conjugations in 2D conformal field theory and holographic bit threads

Mintchev

Tonni

2022

J. High Energ. Phys.

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We study the geometric action of some modular conjugations in two dimensional (2D) conformal field theories. We investigate the bipartition given by an interval when the system is in the ground state, either on the line or on the circle, and in the thermal Gibbs state on the line. We find that the restriction of the corresponding inversion maps to a spatial slice is obtained also in the gauge/gravity correspondence through the geodesic bit threads in a constant time slice of the dual static asymptotically AdS background. For a conformal field theory in the thermal state on the line, the modular conjugation suggests the occurrence of a second world which can be related through the geodesic bit threads to the horizon of the BTZ black brane background. An inversion map is constructed also for the massless Dirac fermion in the ground state and on the line bipartite by the union of two disjoint intervals.

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Looking Beyond the Thermal Horizon: Hidden Symmetries in Chiral Models

Cited by 23 publications

References 9 publications

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

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

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

Modular conjugations in 2D conformal field theory and holographic bit threads

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