On the holographic renormalization group

Boer, Jan de; Verlinde, Erik; Verlinde, Herman

doi:10.1088/1126-6708/2000/08/003

Cited by 692 publications

(1,198 citation statements)

References 43 publications

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“…This expression applies for z d w d > 0, i.e. both points on the same side of the wall, but not 11 We are grateful to the authors of [34] for pointing us to the work of McAvity and Osborn and for prompting us to check that our calculation is consistent with their results. 12 We use ξ here to conform with the notation of [33].…”

Section: Janus Two-point Functions Vs Boundary Cftmentioning

confidence: 58%

Correlation Functions in Holographic RG Flows

Papadimitriou¹,

Skenderis²

2004

J. High Energy Phys.

201

341

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Abstract:We discuss the computation of correlation functions in holographic RG flows.The method utilizes a recently developed Hamiltonian version of holographic renormalization and it is more efficient than previous methods. A significant simplification concerns the treatment of infinities: instead of performing a general analysis of counterterms, we develop a method where only the contribution of counterterms to any given correlators needs to be computed. For instance, the computation of renormalized 2-point functions requires only an analysis at the linearized level. We illustrate the method by discussing flat and AdS-sliced domain walls. In particular, we discuss correlation functions of the Janus solution, a recently discovered non-supersymmetric but stable AdS-sliced domain wall.

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Section: Janus Two-point Functions Vs Boundary Cftmentioning

confidence: 58%

Correlation Functions in Holographic RG Flows

Papadimitriou¹,

Skenderis²

2004

J. High Energy Phys.

201

341

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“…The Brown-York stress tensors mentioned above are now understood as the holographic stress tensors for the dual field theory in one lower dimension. Indeed, the correspondence identifies the radial direction (say in Arnowitt-Deser-Misner coordinates) in an asymptotically AdS space-time with the renormalization group (RG) scale of the dual theory [13][14][15]. Placing an effective boundary at some radial location therefore represents an ultraviolet cutoff in the dual theory where RG initial conditions can be specified.…”

Section: Mach's Principlementioning

confidence: 99%

Mach’s holographic principle

Khoury

Parikh

2009

Phys. Rev. D

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Mach's principle is the concept that inertial frames are determined by matter. We propose and implement a precise formulation of Mach's principle in which matter and geometry are in one-to-one correspondence. Einstein's equations are not modified and no selection principle is applied to their solutions; Mach's principle is realized wholly within Einstein's general theory of relativity. The key insight is the observation that, in addition to bulk matter, one can also add boundary matter. Specification of both boundary and bulk stress tensors uniquely specifies the geometry and thereby the inertial frames. Our framework is similar to that of the black hole membrane paradigm and, in asymptotically AdS space-times, is consistent with holographic duality. I. MACH'S PRINCIPLEAcceleration appears absolute. A snapshot of a rotating bucket of water reveals, through the gentle curve in the water's surface, that the bucket was rotating. Two rocks tied with a rope and set spinning about an axis perpendicular to the rope are measurably distinct from the same two rocks undergoing linear motion: the rope becomes tense. A passenger in an elevator or a windowless spaceship is aware of starts and stops even though the vehicle is a closed system.With his principle of equivalence, Einstein recognized that gravity was simply acceleration in disguise. Moreover, Einstein's equations, like Newton's law of gravitation, indicate that matter is the source for gravity. But if acceleration and gravity are linked, and if gravity

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“…Further refinements include the addition of local counterterms to the action [11] [28] which cancel the divergences arising when going to the boundary. We also mention the work on holographic renormalization group flows from deformations on AdS which extends the AdS/CFT correspondence to non-conformal field theories [29] [30][31] [32]. In this work, we concentrate on the formulation of the scalar field theory on AdS spaces in both minimally and non-minimally coupled cases.…”

Section: Introductionmentioning

confidence: 99%

Energy and the AdS/CFT correspondence

Minces

Rivelles

2001

J. High Energy Phys.

144

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We consider a scalar field theory on AdS in both minimally and non-minimally coupled cases. We show that there exist constraints which arise in the quantization of the scalar field theory on AdS which cannot be reproduced through the usual AdS/CFT prescription. We argue that the usual energy, defined through the stress-energy tensor, is not the natural one to be considered in the context of the AdS/CFT correspondence. We analyze a new definition of the energy which makes use of the Noether current corresponding to time displacements in global coordinates. We compute the new energy for Dirichlet, Neumann and mixed boundary conditions on the scalar field and for both the minimally and non-minimally coupled cases. Then, we perform the quantization of the scalar field theory on AdS showing that, for 'regular' and 'irregular' modes, the new energy is conserved, positive and finite. We show that the quantization gives rise, in a natural way, to a generalized AdS/CFT prescription which maps to the boundary all the information contained in the bulk. In particular, we show that the divergent local terms of the on-shell action contain information about the Legendre transformed generating functional, and that the new constraints for which the irregular modes propagate in the bulk are the same constraints for which such divergent local terms cancel out. In this situation, the addition of counterterms is not required. We also show that there exist particular cases for which the unitarity bound is reached, and the conformal dimension becomes independent of the effective mass. This phenomenon has no bulk counterpart.

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On the holographic renormalization group

Cited by 692 publications

References 43 publications

Correlation Functions in Holographic RG Flows

Correlation Functions in Holographic RG Flows

Mach’s holographic principle

Energy and the AdS/CFT correspondence

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