BMS field theory and holography in asymptotically flat space-times

Dappiaggi, Claudio

doi:10.1088/1126-6708/2004/11/011

Cited by 23 publications

(23 citation statements)

References 30 publications

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“…The little group is the same as in the case of massless Poincaré particles. As a matter of facts, in the space of characters of G BM S , where a generalisation of Mackey machinery works [MC72-75, AD05,Da04,Da05,Da06] (notice that G BM S is not locally compact), there is a a notion of mass, m BM S , which is invariant under the action of G BM S . It turns out that the found G BM S representation is defined over an orbit in the space of characters with m BM S = 0.…”

Section: Introductionmentioning

confidence: 99%

Quantum Out-States Holographically Induced by Asymptotic Flatness: Invariance under Spacetime Symmetries, Energy Positivity and Hadamard Property

Moretti

2008

Commun. Math. Phys.

109

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Abstract. This paper continues the analysis of the quantum states introduced in previous works and determined by the universal asymptotic structure of four-dimensional asymptotically flat vacuum spacetimes at null infinity M . It is now focused on the quantum state λM , of a massless conformally coupled scalar field φ propagating in M . λM is "holographically" induced in the bulk by the universal BMS-invariant state λ defined on the future null infinity + of M . It is done by means of the correspondence between observables in the bulk and those on the boundary at future null infinity discussed in previous papers. This induction is possible when some requirements are fulfilled, in particular whenever the spacetime M and the associated unphysical one,M , are globally hyperbolic and M admits future time infinity i + . λM coincides with Minkowski vacuum if M is Minkowski spacetime. It is now proved that, in the general case of a curved spacetime M , the state λM enjoys the following further remarkable properties. (i) λM is invariant under the (unit component of the Lie) group of isometries of the bulk spacetime M .(ii) λM fulfills a natural energy-positivity condition with respect to every notion of Killing time (if any) in the bulk spacetime M : If M admits a time-like Killing vector, the associated one-parameter group of isometries is represented by a strongly-continuous unitary group in the GNS representation of λM . The unitary group has positive self-adjoint generator without zero modes in the one-particle space. In this case λM is a so-called regular ground state. (iii) λM is (globally) Hadamard in M and thus it can be used as starting point for perturbative renormalisation procedure of QFT of φ in M .

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Section: Introductionmentioning

confidence: 99%

Quantum Out-States Holographically Induced by Asymptotic Flatness: Invariance under Spacetime Symmetries, Energy Positivity and Hadamard Property

Moretti

2008

Commun. Math. Phys.

109

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“…A discussion of the ASG for asymptotically flat spacetimes can be found in Ref. [29]. The previously discussed Weyl transformation maps the I ± boundary of the Schwarzschild spacetime into the I ± inner boundary of our 2D spacetime, hence we can equivalently consider the ASG of our model (3) for x → 0.…”

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confidence: 99%

Statistical Entropy of the Schwarzschild Black Hole

Cadoni

2006

Mod. Phys. Lett. A

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We derive the statistical entropy of the Schwarzschild black hole by considering the asymptotic symmetry algebra near the I − boundary of the spacetime at past null infinity. Using a two-dimensional description and the Weyl invariance of black hole thermodynamics this symmetry algebra can be mapped into the Virasoro algebra generating asymptotic symmetries of anti-de Sitter spacetime. Using lagrangian methods we identify the stress-energy tensor of the boundary conformal field theory and we calculate the central charge of the Virasoro algebra. The Bekenstein-Hawking result for the black hole entropy is regained using Cardy's formula. Our result strongly supports a non-local realization of the holographic principle Black holes can be understood as thermodynamical systems with characteristic temperature and entropy [1,2]. In the last decade a lot of effort has been devoted to understand the microscopic origin of black hole thermodynamics. A detailed microscopical explanation of the thermodynamical properties of black holes would represent not only an important tool for understanding the quantum behavior of gravity but also a way to give a fundamental meaning to the holographic principle [3,4]. A variety of approaches have been used to explain the microscopical origin of the Bekenstein-Hawking entropy: string theoretical (D-Brane) approaches [5,6,7,8,9], methods based on loop quantum gravity [10], induced gravity [11,12], asymptotic symmetries [13,14,15,16,17,18,19,20,21,22,23] and canonical quantization [24]. None of these derivations can be considered as completely satisfactory. In some cases the computation works only for a restrict class of solutions, e.g supersymmetric or asymptotically Anti-de Sitter (AdS) solutions. In other cases the origin of the microscopic degrees of freedom responsible for the black hole entropy is completely obscure. Nonetheless, the fact that completely independent methods give more or less the same (right) answer strongly indicates that the computation of the statistical black hole entropy can be performed without detailed knowledge of the physics governing the microscopical degrees of freedom.If this is the case the statistical black hole entropy should be explained in terms of fundamental features (e.g symmetries) of the "emergent" classical theory of gravity of which black holes are solutions. The most natural realization of this scenario is represented by near-horizon conformal symmetries controlling the black hole entropy trough Cardy's formula for the density of states [21,23]. Carlip has pointed out the main ingredients to be used in this approach: a) Near-horizon conformal symmetries, b) Asymptotic symmetries, c) Canonical realization of the symmetries, d) Horizon constraints [21]. However, the approach of Carlip has some drawbacks. To avoid the complications of the Hamiltonian formulation with a null slicing one has to consider a distorted, "almost" null, horizon [21,23]. The null limit of this formulation is usually singular and the null normal does not have a unique normal...

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“…Since it will play a key role in the forthcoming analysis, we give now some sketches of its main properties (see also [4] and section 2 in [11]); thus, a four dimensional Lorentzian manifold (M 4 ,g µν ), is called asymptotically flat at null infinity if it exists a second manifold (M 4 , g µν ), an embedding i :M 4 → M 4 and a real positive scalar function Ω -the compactification factor -such that…”

Section: Bms Field Theory: Formulationmentioning

confidence: 99%

“…In this latter context a free field is defined as a wave function transforming under a unitary and irreducible representation of SL(2, C) T 4 and, in our approach, we stick to this idea only substituting Poincaré with BMS invariance. In this paper we will not discuss all the techniques which allow us to concertise the above programme leaving instead an interested reader to [7,11] where all the mathematical details are dealt with. Conversely, here, we only point out the key ingredients namely:…”

Section: Bms Field Theory: Formulationmentioning

confidence: 99%

“…Starting from these premises, in [11], we have proposed to combine the null surface formulation of general relativity with BMS field theory in order to concretely implement the holographic paradigm. In particular we conjectured that, not only the geometrical information of a fixed bulk spacetime is encoded in the supertranslations determined by means of the null surface construction, but also the data from matter fields are encoded in the BMS wave functions whose support (which lies in the set of supertranslation or of supermomenta) is compatible with the prescriptions given by the light cone equation.…”

Section: Reconstruction Of Bulk Data: a Conjecturementioning

confidence: 99%

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BMS field theory and the open roads

Dappiaggi

2006

J. Phys.: Conf. Ser.

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Abstract.We develop the basic ingredients of a field theory intrinsically defined on the null infinity boundary of an asymptotically flat spacetime. We also discuss some recent related results and open questions. IntroductionThe last decade witnessed several proposals to solve the long standing quest to formulate a satisfactory quantum version of Einstein theory. Compared to previous attempts, the most recent ones are characterized by the ubiquitous presence of a new paradigm: "the holographic principle". Its origin can be traced back to the seminal paper by G. 't Hooft [1] who remarked that one of the main obstruction in the quantization of general relativity lies in the existence of sources of extreme gravitational fields i.e. black holes. The peculiarity of such objects can be appreciated already studying their behaviour at a classical level and in particular the three laws of black hole thermodynamic. Within this context, the most striking property originates from the Bekenstein formula which relates the entropy S of a black hole to a quarter 1 of the area of its event horizon. From a mere classical perspective this relation is rather counterintuitive since the entropy of a common physical system is proportional to the volume of the region of spacetime where it evolves. Furthermore, if we add to this reasoning, the remark that S can be read as a measure of the degrees of freedom accessible to the system itself, we have the key ingredients leading 't Hooft to claim the following: S =

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BMS field theory and holography in asymptotically flat space-times

Cited by 23 publications

References 30 publications

Quantum Out-States Holographically Induced by Asymptotic Flatness: Invariance under Spacetime Symmetries, Energy Positivity and Hadamard Property

Quantum Out-States Holographically Induced by Asymptotic Flatness: Invariance under Spacetime Symmetries, Energy Positivity and Hadamard Property

Statistical Entropy of the Schwarzschild Black Hole

BMS field theory and the open roads

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