# Algebraic Holography

@article{Rehren2000AlgebraicH, title={Algebraic Holography}, author={Karl-Henning Rehren}, journal={Annales Henri Poincar{\'e}}, year={2000}, volume={1}, pages={607-623} }

Abstract. A rigorous (and simple) proof is given that there is a one-to-one correspondence between causal anti-deSitter covariant quantum field theories on anti-deSitter space and causal conformally covariant quantum field theories on its conformal boundary. The correspondence is given by the explicit identification of observables localized in wedge regions in anti-deSitter space and observables localized in double-cone regions in its boundary. It takes vacuum states into vacuum states, and…

## Figures from this paper

## 89 Citations

Algebraic Holography in Asymptotically Simple, Asymptotically AdS Space-times

- Physics, Mathematics
- 2005

We describe a general geometric setup allowing a generalization of Rehren duality to asymptotically anti-de Sitter space-times whose classical matter distribution is sufficiently well-behaved to…

A mechanism for holography for non-interacting fields on anti-de Sitter spacetimes

- Physics, MathematicsClassical and Quantum Gravity
- 2019

In the setting of non-interacting Klein-Gordon fields on asymptotically anti-de Sitter spacetimes, we show that algebras of observables localized in a neighborhood of the boundary are subalgebras of…

Holographic representation of local bulk operators

- Physics
- 2006

The Lorentzian anti-de Sitter/conformal field theory correspondence implies a map between local operators in supergravity and nonlocal operators in the CFT. By explicit computation we construct CFT…

Intertwining Operator Realization of anti de Sitter Holography

- Mathematics, Physics
- 2015

We give a group-theoretic interpretation of relativistic holography as equivalence between representations of the anti-de Sitter algebra describing bulk fields and boundary fields. Our main result is…

Renormalization group flow in algebraic holography

- Physics
- 2003

Abstract An approach to the Holographic Renormalization Group in the context of Rehren duality — a structural form of the AdS-CFT correspondence, in the context of Local Quantum Physics (Algebraic…

Algebraic Conformal Quantum Field Theory in Perspective

- Physics, Mathematics
- 2015

Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developed in two spacetime dimensions, where many rigorous constructions…

A geometrical origin for the covariant entropy bound

- Physics
- 2003

Causal diamond-shaped subsets of spacetime are naturally associated with operator algebras in quantum field theory, and they are also related to the Bousso covariant entropy bound. In this work we…

Generalized Free Fields and the AdS-CFT Correspondence

- Mathematics, Physics
- 2003

Abstract.
Motivated by structural issues in the AdS-CFT correspondence, the theory
of generalized free fields is reconsidered. A stress-energy tensor for the generalized
free field is constructed as…

Holography, SL(2,R) symmetry, Virasoro algebra and all that in Rindler spacetime

- Mathematics
- 2003

It is shown that it is possible to define quantum field theory of a massless scalar free field on the event horizon of a 2D-Rindler spacetime. Free quantum field theory on the horizon enjoys…

Deformations of Quantum Field Theories on Spacetimes with Killing Vector Fields

- Physics, Mathematics
- 2010

The recent construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of curved spacetimes. These spacetimes carry a family of wedge-like…

## References

SHOWING 1-10 OF 18 REFERENCES

Anti-de Sitter space and holography

- Physics
- 1998

Recently, it has been proposed by Maldacena that large $N$ limits of certain conformal field theories in $d$ dimensions can be described in terms of supergravity (and string theory) on the product of…

Current Trends in Axiomatic Quantum Field Theory

- Mathematics, Physics
- 1998

In this article a non-technical survey is given of the present status of Axiomatic Quantum Field Theory and interesting future directions of this approach are outlined. The topics covered are the…

On the duality condition for a Hermitian scalar field

- Mathematics
- 1975

A general Hermitian scalar field, assumed to be an operator−valued tempered distribution, is considered. A theorem which relates certain complex Lorentz transformations to the TCP transformation is…

Modular structure of the local algebras associated with the free massless scalar field theory

- Mathematics
- 1982

The modular structure of the von Neumann algebra of local observables associated with a double cone in the vacuum representation of the free massless scalar field theory of any number of dimensions…

Global conformal invariance in quantum field theory

- Mathematics
- 1975

AbstractSuppose that there is given a Wightman quantum field theory (QFT) whose Euclidean Green functions are invariant under the Euclidean conformal group⋍SOe(5,1). We show that its Hilbert space of…

The Large-N Limit of Superconformal Field Theories and Supergravity

- Physics
- 1997

We show that the large-N limits of certainconformal field theories in various dimensions includein their Hilbert space a sector describing supergravityon the product of anti-de Sitter spacetimes,…

Intertwining operator realization of the AdS/CFT correspondence

- Physics
- 1999

We give a group-theoretic interpretation of the AdS/CFT correspondence as relation of representation equivalence between representations of the conformal group describing the bulk AdS fields φ their…

Dimensional Reduction in Quantum Gravity

- Physics, Mathematics
- 1993

The requirement that physical phenomena associated with gravitational collapse should be duly reconciled with the postulates of quantum mechanics implies that at a Planckian scale our world is not…

JONES-WASSERMANN SUBFACTORS FOR DISCONNECTED INTERVALS

- Mathematics
- 1997

We show that the Jones-Wassermann subfactors for disconnected intervals, which are constructed from the representations of loop groups of type A, are finite-depth subfactors. The index value and the…

The world as a hologram

- Physics
- 1994

According to ’t Hooft the combination of quantum mechanics and gravity requires the three‐dimensional world to be an image of data that can be stored on a two‐dimensional projection much like a…