Holography beyond conformal invariance and AdS isometry?

Abstract

We suggest that the principle of holographic duality can be extended beyond conformal invariance and AdS isometry. Such an extension is based on a special relation between functional determinants of the operators acting in the bulk and on its boundary, provided that the boundary operator represents the inverse propagators of the theory induced on the boundary by the Dirichlet boundary value problem from the bulk spacetime. This relation holds for operators of general spin-tensor structure on generic manifolds with boundaries irrespective of their background geometry and conformal invariance, and it apparently underlies numerous $O(N^0)$ tests of AdS/CFT correspondence, based on direct calculation of the bulk and boundary partition functions, Casimir energies and conformal anomalies. The generalized holographic duality is discussed within the concept of the "double-trace" deformation of the boundary theory, which is responsible in the case of large $N$ CFT coupled to the tower of higher spin gauge fields for the renormalization group flow between infrared and ultraviolet fixed points. Potential extension of this method beyond one-loop order is also briefly discussed.

arXiv comment16 pages, LaTeX, prepared for a special issue of JETP dedicated to the 60th birthday of Valery Rubakov

References in corpus (22)

• An Alternative to Compactification
• 4D Gravity on a Brane in 5D Minkowski Space
• The dS/CFT Correspondence
• AdS Dual of the Critical O(N) Vector Model
• Cosmology on a Brane in Minkowski Bulk
• On Renormalization Group Flows in Four Dimensions
• Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings
• A universal result on central charges in the presence of double-trace deformations
• One Loop Tests of Higher Spin AdS/CFT
• Functional determinants by contour integration methods
• Double-trace operators and one-loop vacuum energy in AdS/CFT
• Partition functions and double-trace deformations in AdS/CFT
• On partition function and Weyl anomaly of conformal higher spin fields
• AdS Description of Induced Higher-Spin Gauge Theory
• Partition Functions and Casimir Energies in Higher Spin AdS_{d+1}/CFT_d
• Graviton 1-loop partition function for 3-dimensional massive gravity
• Cosmological Landscape From Nothing: Some Like It Hot
• Operator algebra of free conformal currents via twistors
• Towards higher-spin holography in ambient space of any dimension
• Anomaly Driven Cosmology: Big Boost Scenario and AdS/CFT Correspondence
• Quantum Effective Action in Spacetimes with Branes and Boundaries
• Quantum Effective Action in Spacetimes with Branes and Boundaries: Diffeomorphism Invariance

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• Sakharov's induced gravity on the AdS background: SM scale as inverse mass parameter of the Schwinger-DeWitt expansion
• On the Weyl anomaly of 4D Conformal Higher Spins: a holographic approach
• Simple way to calculate UV-finite one-loop quantum energy in Randall-Sundrum model