Geometric Holography, the Renormalization Group and the c-Theorem

Cesar Gomez; Enrique Alvarez

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Geometric Holography, the Renormalization Group and the c-Theorem

Enrique Alvarez, Cesar Gomez

High Energy Physics - Theory · Submitted 30 Jul 1998

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

The authors' main claim By studying the renormalization group flow along null geodesic congruences a holographic version of Zamolodchikov's c-theorem is proven.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.04 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.11 · mentions code or data availability 0.02.

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In this paper the whole geometrical set-up giving a conformally invariant holographic projection of a diffeomorphism invariant bulk theory is clarified. By studying the renormalization group flow along null geodesic congruences a holographic version of Zamolodchikov's c-theorem is proven.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this paper the whole geometrical set-up giving a conformally invariant holographic projection of a diffeomorphism invariant bulk theory is clarified.	contribution 0.95	0.80	0.13	asserted 1.00
s1	By studying the renormalization group flow along null geodesic congruences a holographic version of Zamolodchikov's c-theorem is proven.	result 0.89	0.92	0.75	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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figures and tables
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S sections
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C citations
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The paper

Original abstract

In this paper the whole geometrical set-up giving a conformally invariant holographic projection of a diffeomorphism invariant bulk theory is clarified. By studying the renormalization group flow along null geodesic congruences a holographic version of Zamolodchikov's c-theorem is proven.

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References

Forward citations

Cited by 12 Pith papers

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

Renormalization Group Flows from Holography--Supersymmetry and a c-Theorem
hep-th 1999-04 accept novelty 8.0 of 10

An explicit supersymmetric kink in five-dimensional gauged supergravity realizes a holographic renormalization group flow and yields a monotonic c-function that matches trace anomaly coefficients at both endpoints.
Covariant unification of holographic c-functions
hep-th 2026-05 unverdicted novelty 7.0 of 10

A new covariant c-function is defined from extrinsic curvature of codimension-two bulk slices, unifying prior foliation-based definitions and exhibiting expected monotonic behavior in conformal, confining, and mixed-g...
Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm
hep-th 2010-10 accept novelty 7.0 of 10

Integrating out high-energy modes in a strongly coupled field theory with a gravity dual is shown to correspond to integrating out a slice of the bulk geometry, yielding a Wilsonian flow equation for the boundary effe...
$SO(1, d + 1)$ symmetry of the Exact RG equation
hep-th 2026-01 conditional novelty 6.0 of 10

The ERG evolution operator is SO(1,d+1)-invariant for any admissible cutoff, with cutoff-dependent conformal generators that reduce to standard AdS isometries for the special AdS-mapping cutoff.
Yang-Mills interaction from boundary vector model
hep-th 2025-04 conditional novelty 6.0 of 10

The ERG flow of the USp(2N) singlet sector of a free 3D U(2N) scalar theory yields a bulk AdS4 cubic action that is on-shell equivalent to Yang-Mills plus a field-strength-cubed term.

Show 7 more citing papers

de Sitter extremal surfaces
hep-th 2015-01 conditional novelty 6.0 of 10

In de Sitter space, real minimal-area extremal surfaces are null past-lightcone wedges with zero area, while complex extremal surfaces have area matching the dS/CFT central charge.
On the Holographic Renormalization Group
hep-th 1999-12 conditional novelty 6.0 of 10

The radial evolution equations of five-dimensional supergravity take the form of Callan-Symanzik equations, identifying the classical supergravity action with the quantum effective action of the dual gauge theory.
Compactifications of the Klebanov-Witten CFT and new $AdS_3$ backgrounds
hep-th 2015-03 conditional novelty 5.0 of 10

Non-Abelian T-duality applied to the Klebanov-Witten CFT compactified on a Riemann surface produces new smooth AdS3 supergravity backgrounds in Type IIA, Type IIB and M-theory, together with holographic observables fo...
UV/IR Relations in AdS Dynamics
hep-th 1998-09 accept novelty 5.0 of 10

The two distance-energy relations used in AdS/CFT coincide only in conformal backgrounds; for nonconformal Dp-branes they differ in functional form, so holographic and brane-probe reasoning can disagree about which ef...
Krylov Complexity and $c$-function along RG Flows
hep-th 2026-08 conditional novelty 4.0 of 10

Along holographic RG flows, the acceleration of spread complexity and the covariant c-function are algebraically related: inversely in fixed-dimension domain walls and Dp-branes, co-monotonically in twisted compactifications.
Scale invariance vs conformal invariance
hep-th 2013-02 accept novelty 4.0 of 10

Under stated assumptions, scale invariance is proved to imply conformal invariance in two dimensions, while in four dimensions the enhancement remains a well-supported conjecture with no known counterexample.
Emergent Gravity in a Holographic Universe
hep-th 2019-08 conditional novelty 3.0 of 10

Causal diamonds in symmetric spacetimes obey a thermodynamic first law with negative temperature, and the Einstein equations can be recast as an entropy equilibrium condition, with a long-string CFT picture for non-Ad...

How the literature uses it

34 arXiv papers cite this in 37 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 3 papers

We prove a c-theorem for holographic theories.

The Holographic Principle and the Renormalization Group · 0.99
Then, we prove the Zamolodchikov C-theorem holographically.

AdS/CFT Duality and Holographic Renormalization Group: A Review · 0.97
We state a c-theorem with respect to this quantity and prove it.

Holography, a covariant c-function, and the geometry of the renormalization group · 0.96

Papers citing it · 17 sentences without a confident label

Uses its method or tool 1 paper

In this section we present an alternative holographic $c$-function for our models, following the proposal of [ref] , based on ideas of [ref] , which proposed to use the expansion parameter of the congruences of null geodesics to extract the information encoded holographically in the geometry (see also [ref] for a similar proposal for the $c$-function).

Holographic spontaneous anisotropy · $c$-function from null congruences · 0.87

Cites it as background 19 papers

For the classical renormalization group flows, [ref] established a c-theorem, demonstrating that so long as the bulk geometry satisfied a suitable energy condition, the c-function of [ref] would be monotonically decreasing along the flow from the UV to the IR (see also [ref] ).

Reversing Renormalization-Group Flows with AdS/CFT · Introduction · 0.90
For systems with a gravity dual, the AdS/CFT correspondence [ref] provides a striking geometric picture for the renormalization group flow and the resulting low energy behavior; the radial direction in the bulk can be associated with the energy scale of the boundary theory [ref] , and the radial flow in the bulk geometry can be interpreted as the renormalization group flow of the boundary theory [ref] .

Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm · Introduction · 0.97
A covariant construction based on the expansion of null congruences was proposed in [ref] ; see also [ref] .

Covariant unification of holographic c-functions · Introduction · 0.83

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