Holographic Renormalization and Ward Identities with the Hamilton-Jacobi Method

Dario Martelli; Wolfgang Mueck

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Holographic Renormalization and Ward Identities with the Hamilton-Jacobi Method

Dario Martelli, Wolfgang Mueck

High Energy Physics - Theory · Submitted 7 May 2002

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In particular, we demonstrate the breaking of U(1)_R current conservation, recovering the holographic chiral anomaly recently discussed in hep-th/0112119 and hep-th/0202056.

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arXiv IDhep-th/0205061 (version 2)

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CitationDario Martelli, Wolfgang Mueck. "Holographic Renormalization and Ward Identities with the Hamilton-Jacobi Method." arXiv:hep-th/0205061 (2002). https://pith.science/paper/DD3RKIHW

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.56 · mentions code or data availability 0.02.

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A systematic procedure for performing holographic renormalization, which makes use of the Hamilton-Jacobi method, is proposed and applied to a bulk theory of gravity interacting with a scalar field and a U(1) gauge field in the Stueckelberg formalism. We describe how the power divergences are obtained as solutions of a set of "descent equations" stemming from the radial Hamiltonian constraint of the theory. In addition, we isolate the logarithmic divergences, which are closely related to anomalies. The method allows to determine also the exact one-point functions of the dual field theory. Using the other Hamiltonian constraints of the bulk theory, we derive the Ward identities for diffeomorphisms and gauge invariance. In particular, we demonstrate the breaking of U(1)_R current conservation, recovering the holographic chiral anomaly recently discussed in hep-th/0112119 and hep-th/0202056.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A systematic procedure for performing holographic renormalization, which makes use of the Hamilton-Jacobi method, is proposed and applied to a bulk theory of gravity interacting with a scalar field and a U(1) gauge field in the Stueckelberg formalism.	contribution 0.90	0.92	0.32	asserted 1.00
s1	We describe how the power divergences are obtained as solutions of a set of "descent equations" stemming from the radial Hamiltonian constraint of the theory.	method 0.91	0.92	0.08	asserted 1.00
s2	In addition, we isolate the logarithmic divergences, which are closely related to anomalies.	contribution 0.47	0.90	0.07	asserted 1.00
s3	The method allows to determine also the exact one-point functions of the dual field theory.	result 0.55	0.88	0.14	asserted 0.91
s4	Using the other Hamiltonian constraints of the bulk theory, we derive the Ward identities for diffeomorphisms and gauge invariance.	contribution 0.46	0.95	0.16	asserted 1.00
s5	In particular, we demonstrate the breaking of U(1)_R current conservation, recovering the holographic chiral anomaly recently discussed in hep-th/0112119 and hep-th/0202056.	result 0.98	0.86	0.29	asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.99 · evidence from proof or derivation 1.00.

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Original abstract

A systematic procedure for performing holographic renormalization, which makes use of the Hamilton-Jacobi method, is proposed and applied to a bulk theory of gravity interacting with a scalar field and a U(1) gauge field in the Stueckelberg formalism. We describe how the power divergences are obtained as solutions of a set of "descent equations" stemming from the radial Hamiltonian constraint of the theory. In addition, we isolate the logarithmic divergences, which are closely related to anomalies. The method allows to determine also the exact one-point functions of the dual field theory. Using the other Hamiltonian constraints of the bulk theory, we derive the Ward identities for diffeomorphisms and gauge invariance. In particular, we demonstrate the breaking of U(1)_R current conservation, recovering the holographic chiral anomaly recently discussed in hep-th/0112119 and hep-th/0202056.

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References

Forward citations

Cited by 15 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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Flat Holography & Holographic Renormalization: Scalar Field
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A Hamilton-Jacobi holographic renormalization scheme for scalars in Minkowski space yields a GKPW-style flat holography dictionary: source = scattering data, vev = renormalized momentum, with correlators matching the ...
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For m²L²=-2 in AdS black holes with integrable mixed boundary conditions, the cubic coefficient in the near-boundary expansion of the solution-dependent W(φ) is fixed by the boundary deformation to ensure a well-posed...
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A higher-dimensional generalization of the TTbar deformation is shown to reproduce semiclassical gravity in anti-de Sitter space truncated at a finite radial cutoff, matching spectra, thermodynamics, and correlation f...

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A recursive algorithm built on two commuting functional operators generates the full holographic dictionary, including counterterms, Fefferman-Graham expansions, Ward identities and anomalies, for asymptotically local...
Holographic Renormalization of general dilaton-axion gravity
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A recursive algorithm solves the radial Hamilton-Jacobi equation in a derivative expansion, yielding explicit boundary counterterms for general dilaton-axion gravity up to five dimensions and generalized Fefferman-Gra...
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How the literature uses it

32 arXiv papers cite this in 46 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 24 sentences without a confident label

Uses its method or tool 9 papers

Our algorithm for constructing the holographic dictionary hinges upon a certain asymptotic solution of the radial Hamilton-Jacobi (HJ) equation [ref] , subject to asymptotically Lif or hvLf boundary conditions.

Lifshitz holography: The whole shebang · Introduction · 0.91
The derivation starts with the Hamilton-Jacobi equation in the bulk, and uses the techniques of holographic renormalization developed in [ref] .

Holography at finite cutoff with a $T^2$ deformation · Introduction · 1.00
This idea was systematically developed in [ref] with Papadimitriou prescribing a recursive algorithm [ref] (see [ref] for an online lecture) that we follow closely here.

A note on holographic renormalization for non-conformal branes by recursion · Introduction · 0.90

Compares with it 1 paper

The results are reminiscent of the counterterms used in the AdS/CFT correspondence [ref] , but there are also significant differences.

Boundary Terms Unbound! Holographic Renormalization of Asymptotically Linear Dilaton Gravity · Explicit Counterterms · 0.93

Cites it as background 11 papers

A direct correspondence between supergravity equations of motion and renormalization group equations has been described later in [ref] and [ref] in terms of descent equations following from the Hamiltonian-Jacobi method where the radial direction plays the role of the evolution parameter (for a review see [ref] ).

Holographic RG flows and boundary conditions in a 3D gauged supergravity · Introduction · 0.89
There exist various methods in the literature for such a task: the Hamiltonian method [ref] , the quasilocal Brown-York formalism [ref] , the holographic renormalization [ref] or the Hamilton-Jacobi approach [ref] .

Holographic renormalization and the variational problem for mixed boundary conditions via a solution-dependent superpotential-like function · Introduction · 0.93
This program, renormalization in the bulk, is often coined as “holographic renormalization” and is a standard approach for computing interesting observable functions within AdS/CFT [ref] .

A note on holographic renormalization for non-conformal branes by recursion · Introduction · 0.92

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