Gauge invariant two-point vertices of shadow fields, AdS/CFT, and conformal fields

R.R. Metsaev

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Gauge invariant two-point vertices of shadow fields, AdS/CFT, and conformal fields

R.R. Metsaev

High Energy Physics - Theory · Submitted 27 Jul 2009

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The authors' main claim Also we shown that the bulk action evaluated on solution of the Dirichlet problem leads to new description of conformal fields.

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In the framework of gauge invariant Stueckelberg approach, totally symmetric arbitrary spin shadow fields in flat space-time of dimension greater than or equal to four are studied. Gauge invariant two-point vertices for such shadow fields are obtained. We demonstrate that, in Stueckelberg gauge frame, these gauge invariant vertices become the standard two-point vertices of CFT. Light-cone gauge two-point vertices of the shadow fields are also obtained. AdS/CFT correspondence for the shadow fields and the non-normalizable solutions of free massless totally symmetric arbitrary spin AdS fields is studied. AdS fields are considered in a modified de Donder gauge and this simplifies considerably the study of AdS/CFT correspondence. We demonstrate that the bulk action, when it is evaluated on solution of the Dirichlet problem, leads to the two-point gauge invariant vertex of shadow field. Also we shown that the bulk action evaluated on solution of the Dirichlet problem leads to new description of conformal fields. The new description involves Stueckelberg gauge symmetries and gives simple higher-derivative Lagrangian for the conformal arbitrary spin field. In the Stueckelberg gauge frame, our Lagrangian becomes the standard Lagrangian of conformal field. Light-cone gauge Lagrangian of the arbitrary spin conformal field is also obtained.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In the framework of gauge invariant Stueckelberg approach, totally symmetric arbitrary spin shadow fields in flat space-time of dimension greater than or equal to four are studied.	contribution 0.75	0.76	0.04	asserted 0.93
s1	Gauge invariant two-point vertices for such shadow fields are obtained.	result 0.87	0.93	0.10	asserted 1.00
s2	We demonstrate that, in Stueckelberg gauge frame, these gauge invariant vertices become the standard two-point vertices of CFT.	result 0.91	0.93	0.24	asserted 1.00
s3	Light-cone gauge two-point vertices of the shadow fields are also obtained.	result 0.85	0.93	0.05	asserted 1.00
s4	AdS/CFT correspondence for the shadow fields and the non-normalizable solutions of free massless totally symmetric arbitrary spin AdS fields is studied.	contribution 0.99	0.83	0.09	asserted 0.89
s5	AdS fields are considered in a modified de Donder gauge and this simplifies considerably the study of AdS/CFT correspondence.	method 0.94	0.74	0.05	asserted 1.00
s6	We demonstrate that the bulk action, when it is evaluated on solution of the Dirichlet problem, leads to the two-point gauge invariant vertex of shadow field.	result 0.98	0.92	0.24	asserted 1.00
s7	Also we shown that the bulk action evaluated on solution of the Dirichlet problem leads to new description of conformal fields.	result 0.97	0.94	0.26	asserted 1.00
s8	The new description involves Stueckelberg gauge symmetries and gives simple higher-derivative Lagrangian for the conformal arbitrary spin field.	result 0.82	0.88	0.25	asserted 1.00
s9	In the Stueckelberg gauge frame, our Lagrangian becomes the standard Lagrangian of conformal field.	result 0.92	0.89	0.18	asserted 1.00
s10	Light-cone gauge Lagrangian of the arbitrary spin conformal field is also obtained.	result 0.85	0.91	0.07	asserted 1.00

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In the framework of gauge invariant Stueckelberg approach, totally symmetric arbitrary spin shadow fields in flat space-time of dimension greater than or equal to four are studied. Gauge invariant two-point vertices for such shadow fields are obtained. We demonstrate that, in Stueckelberg gauge frame, these gauge invariant vertices become the standard two-point vertices of CFT. Light-cone gauge two-point vertices of the shadow fields are also obtained. AdS/CFT correspondence for the shadow fields and the non-normalizable solutions of free massless totally symmetric arbitrary spin AdS fields is studied. AdS fields are considered in a modified de Donder gauge and this simplifies considerably the study of AdS/CFT correspondence. We demonstrate that the bulk action, when it is evaluated on solution of the Dirichlet problem, leads to the two-point gauge invariant vertex of shadow field. Also we shown that the bulk action evaluated on solution of the Dirichlet problem leads to new description of conformal fields. The new description involves Stueckelberg gauge symmetries and gives simple higher-derivative Lagrangian for the conformal arbitrary spin field. In the Stueckelberg gauge frame, our Lagrangian becomes the standard Lagrangian of conformal field. Light-cone gauge Lagrangian of the arbitrary spin conformal field is also obtained.

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Cited by 8 Pith papers

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

AdS Description of Induced Higher-Spin Gauge Theory
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The change in three-sphere free energy from gauging a spin-s symmetry equals (1/2) log N times the number of spin-(s-1) conformal Killing tensors, matching the dual AdS calculation.
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A 2N-field Gaussian boundary model is proposed as the exact Hilbert space of minimal higher spin de Sitter gravity, reproducing the earlier Sp(N) proposal at large N and yielding closed-form late-time correlators.
Partition function of free conformal higher spin theory
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The canonical partition function of free conformal higher-spin theory is computed in closed form for all even dimensions, and the summed Casimir energy vanishes under the regularization that also cancels the conformal...
Holography, Unfolding and Higher-Spin Theory
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The AdS4 higher-spin gauge theory is argued to be dual to a nonlinear 3d conformal higher-spin gauge theory of conserved currents interacting via Chern-Simons fields, escaping the Maldacena-Zhiboedov free-theory theorem.
Effective action in a higher-spin background
hep-th 2010-12 accept novelty 6.0 of 10

The one-loop effective action of a free massless scalar in a higher-spin background is computed perturbatively, with its divergent and finite parts expressed in terms of higher-spin curvatures and linked to conformal ...

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On partition function and Weyl anomaly of conformal higher spin fields
hep-th 2013-09 accept novelty 5.0 of 10

The 4D conformal higher-spin partition function factorizes into partially-massless determinants, yielding spin-s Weyl anomaly coefficients whose bosonic a_s matches an independent AdS/CFT result and whose regularized ...
Notes on the ambient approach to boundary values of AdS gauge fields
hep-th 2012-07 conditional novelty 5.0 of 10

Using a parent (ambient) formulation, the authors give a manifestly o(d,2)-covariant, local description of the boundary behaviour of massless symmetric tensor gauge fields on AdS(d+1), recovering conformal currents, s...
On (Un)Broken Higher-Spin Symmetry in Vector Models
hep-th 2015-12 conditional novelty 4.0 of 10

One-loop anomalous dimensions of higher-spin currents in Wilson-Fisher CFTs are re-derived via multiplet recombination, matching known results, and part of the dual AdS higher-spin cubic action is reconstructed.

How the literature uses it

41 arXiv papers cite this in 57 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 · 37 sentences without a confident label

Builds on it 1 paper

In this paper, we extend the gauge invariant Stueckelberg approach to CFT initiated in Refs. [ref] to the study of anomalous conformal currents and shadow fields.

Gauge invariant approach to low-spin anomalous conformal currents and shadow fields · Conclusions · 1.00

Cites it as background 18 papers

Effective action for arbitrary spin shadow field found in Refs. [ref] was presented in terms of gauge field subject to some differential constraints.

BRST invariant effective action of shadow fields, conformal fields, and AdS/CFT · Introduction · 0.93
) For $d=4$ and $d≥4$, the minimal Lagrangian of the totally symmetric arbitrary spin short conformal field in the Table was obtained in the respective Ref. [ref] and Ref. [ref] (see also Ref. [ref] ).

Long, partial-short, and special conformal fields · Introduction · 0.84
The light-cone and Stuckelberg-like formulations of the aforementioned aspects have been intensively developed by Metsaev over the years [ref] .

Notes on the ambient approach to boundary values of AdS gauge fields · Introduction · 0.95

What it cites · 34 sentences without a confident label

Contests 4 papers

Normalization factor in Ref. [ref] disagrees with our result and results reported in Refs. [ref] .]

Higher-Spin Fields in Braneworlds · AdS/CFT correspondence for arbitrary spin field · contest 0.80
Normalization factor in Ref. [ref] disagrees with our result and results reported in Refs. [ref] .]

Correlation functions in the CFT(d)/AdS(d+1) correpondence · AdS/CFT correspondence for arbitrary spin field · contest 0.80
Normalization factor in Ref. [ref] disagrees with our result and results reported in Refs. [ref] .]

D=4 Super Yang Mills, D=5 gauged supergravity and D=4 conformal supergravity · AdS/CFT correspondence for arbitrary spin field · contest 0.80

Builds on 1 paper

In this paper we develop further our approach initiated in Ref. [ref] .

Shadows, currents and AdS fields · Introduction · 0.99

Uses the method or tool of 4 papers

To discuss the correspondence we use the $CFT$ adapted gauge invariant Lagrangian and modified de Donder gauge condition for the massless arbitrary spin $AdS$ field found in Ref. [ref]

CFT adapted gauge invariant formulation of arbitrary spin fields in AdS and modified de Donder gauge · AdS/CFT correspondence for arbitrary spin field · 0.99
Following the procedure in [ref] , we note that solution of equations 19072009-06 with the Dirichlet problem corresponding to boundary shadow scalar field $ϕ_$ takes the form

Anti De Sitter Space And Holography · AdS/CFT correspondence for scalar field · 0.99
To this end we use $CFT$ adapted gauge invariant Lagrangian and the modified Lorentz gauge condition [ref] (see Appendix [ref]).

CFT adapted gauge invariant formulation of massive arbitrary spin fields in AdS · AdS/CFT correspondence for spin-1 field · 0.99

Uses data or values from 1 paper

The normalization factor in r.h.s. of man2009-02-14072009-02 was found in Ref. [ref] .

Correlation functions in the CFT(d)/AdS(d+1) correpondence · AdS/CFT correspondence for spin-1 field · 0.86

Compares with 8 papers

In the standard formulation of the conformal currents and shadow fields, the operator $R^a$ is equal to zero, while, in the gauge invariant approach, the operator $R^a$ turns out be nontrivial [ref] .

Shadows, currents and AdS fields · Global conformal symmetries · 0.81
Coincidence of our result and the one in Refs. [ref] is related to the fact that we fix boundary value of the Dirichlet problem at $z=0$, compute the effective action at $z=ϵ$ and then scale $ϵ→0$ (see also Ref. [ref] ), while authors of Refs. [ref] fix boundary value of the Dirichlet problem at $z = ϵ$ and, after computation of the effective action, scale $ϵ→0$.

Anti De Sitter Space And Holography · AdS/CFT correspondence for scalar field · 1.00
Coincidence of our result and the one in Refs. [ref] is related to the fact that we fix boundary value of the Dirichlet problem at $z=0$, compute the effective action at $z=ϵ$ and then scale $ϵ→0$ (see also Ref. [ref] ), while authors of Refs. [ref] fix boundary value of the Dirichlet problem at $z = ϵ$ and, after computation of the effective action, scale $ϵ→0$.

Correlation functions in the CFT(d)/AdS(d+1) correpondence · AdS/CFT correspondence for scalar field · 1.00

Cites as background 26 papers

We now briefly review the gauge invariant approach to conformal currents and shadow fields developed in Ref. [ref] .

Shadows, currents and AdS fields · Gauge invariant approach to conformal currents and shadow fields · 0.87
We remind that in the framework of $AdS/CFT$ correspondence [ref] , the conformal currents and shadow fields manifest themselves in two related ways at least.

The Large N Limit of Superconformal Field Theories and Supergravity · Introduction · 0.99
[ For massless arbitrary spin $AdS_5$ fields, the effective action, by using radial gauge, was studied in [ref] .

Higher-Spin Fields in Braneworlds · AdS/CFT correspondence for arbitrary spin field · 0.80

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