Holography of the N=1 Higher-Spin Theory on AdS4

A. C. Petkou; R. G. Leigh

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Holography of the N=1 Higher-Spin Theory on AdS4

R. G. Leigh, A. C. Petkou

High Energy Physics - Theory · Submitted 25 Apr 2003 · 26 references

Pith's verdict: A solid proposal paper: the parity observation is the real contribution, and the identification of the interacting fixed point is argued by analogy rather than derived from the bulk action.

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arXiv IDhep-th/0304217 (version 1)

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CitationA. C. Petkou, R. G. Leigh. "Holography of the N=1 Higher-Spin Theory on AdS4." arXiv:hep-th/0304217 (2003). https://pith.science/paper/DEFEZR77

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Editor's note

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The thing to know up front: this is the N=1 extension of Klebanov-Polyakov, and the part that actually earns its keep is the parity observation in Sections 2-3. The two conformally coupled scalars in the Osp(1|4) Wess-Zumino multiplet carry opposite parity, and that fixes which of the two boundary-condition choices can be represented by free fields. That is a real structural point, not a restatement of [4], and it explains cleanly why one bulk theory can carry both boundary fixed points. The spectrum matching in (3.1)-(3.3) against O(N)-singlet bilinears is straightforward and correct, and the boundary-condition machinery in 4.1-4.2, with the explicit kernels (4.2), (4.3), (4.21), is careful work. The stress-test note is right about where the gap sits, and it is a better location than the reader's version: the parity argument only establishes the negative, that the other choice is not free. Getting from 'not free' to 'the critical O(N) model' is done twice, and neither route is a bulk computation. The double-trace analysis in 5.2 leans on Klebanov-Witten large-N factorization by analogy; the Higgsing story in 5.3 assumes a cubic coupling of the schematic form (5.8) with the right parity, and the paper says outright that the higher-spin interactions are left implicit ('computable, at least in principle', footnote 5). If the actual N=1 interactions do not contain that coupling with that parity, the interacting boundary condition is not distinguished from an arbitrary non-free CFT. The authors are candid about this, so it is not a hidden flaw, but it does mean the central claim is a conjecture supported by consistent structure rather than a derivation. The marginality of (5.1) is likewise flagged as unsettled by the authors themselves. The claim that SUSY-breaking deformations flow to a supersymmetric theory at large N is the most striking thing here and rests entirely on the same boundary-condition logic; worth taking seriously, not established. Who should read it: anyone working on higher-spin holography or the O(N) vector model. It is a foundational reference for the N=1 case, and the parity mechanism has legs beyond this paper. Recommendation: send it out. The proposal is well-posed, the representation theory is checkable, and the gaps are stated rather than papered over. Referees should push on whether (5.8) actually exists in the N=1 theory.

Referee report

Significance

If the proposal holds, it identifies a second, supersymmetric instance of the Klebanov-Polyakov phenomenon in which a single higher-spin theory on AdS4 encodes both phases of a large-N vector model, and it makes the role of parity in that correspondence explicit. The representation-theoretic input is clean and independently checkable: the decompositions (3.1)-(3.3) of singleton products into Osp(1|4) multiplets are matched against the known O(N)-singlet bilinears of the free superfield, and the parity assignments of D(1,0) and D(2,0) are tied to the structure of the supercharge in the Appendix. The paper also states falsifiable consequences, notably that the boundary stress tensor remains conserved for either boundary-condition choice (Section 5.3) and that the deformation (5.1) may be exactly marginal (Section 5.2.2). The work is a proposal argued from consistency rather than a derivation from a known bulk action, and it is candid about that.

Major objections (3)

[Section 5.1.2 and Section 5.3] The central claim of the paper, that one of the two boundary-condition choices gives the *interacting* (critical) N=1 O(N) vector model, is not established by the arguments given. The parity analysis of Sections 2-3 establishes only the negative statement that the choice (regular h(+)1, irregular h(-)2) admits no free-field representation, since the Legendre transform preserves parity and the free bilinears (A.9) require D(1,0) even and D(2,0) odd. 'Not free' does not imply 'the critical O(N) model.' The positive identification is then made in Section 5.1.2 on the grounds that the chosen boundary conditions 'will break the higher-spin gauge symmetry for subleading-N', which is a necessary but not a sufficient condition for the boundary theory to be the interacting fixed point. A concrete test would strengthen this considerably: evaluate the one-loop bulk diagram generated by a coupling of the form (5.8) and compare the resulting O(1/N) anomalous dimension of a higher-spin current with the known large-N values in the critical O(N) vector model. Absent such a check, the identification with the critical point should be stated as a conjecture supported by the deformation analysis, not as a consequence of the boundary conditions.
[Section 4.2 versus Section 5.2.3] There is an internal tension between the discussion of the fermion boundary condition in Section 4.2 and the claim in Section 5.2.3. Equation (4.27), u(E)- = u(0)- + E u(E)+, is described in Section 4.2 as 'a boundary condition that does not preserve parity', and the text states that E -> infinity 'clearly corresponds to switching q and s, and thus we would expect a rearrangement of the supermultiplet, if the theory is supersymmetric at E -> infinity' -- an explicitly conditional statement. Section 5.2.3 then asserts that the supersymmetry-breaking deformation (5.3), with boundary conditions (5.4), leads at large coupling to 'an N=1 supersymmetric theory, at its strongly coupled fixed point', and the Summary elevates this to one of the paper's 'particularly intriguing' results. The two passages need to be reconciled: either the E -> infinity limit of (4.27) reproduces the supersymmetric fermion condition used in Section 5.1.2, in which case Section 4.2 should say so and explain how the parity obstruction is evaded, or it does not, in which case the claim of large-N supersymmetry restoration in Section 5.2.3 does not follow from the stated boundary conditions.
[Section 5.2.2, Section 5.2.3, and Section 5.3] The deformation analysis rests on the Klebanov-Witten large-N factorization of Eq. (4.11), which is a leading-order-in-1/N statement, but the conclusions are phrased without that qualification. In particular, the assertion in Section 5.3 that the two boundary theories have 'exactly the same spectrum of dimensions' at large N should be stated precisely as holding at leading order in 1/N and for the single-trace bilinear sector; the free theory's multi-trace spectrum is not reproduced by the bulk tree-level Wess-Zumino action alone. Likewise, the statement in Section 5.2.3 that a supersymmetry-breaking deformation flows to a supersymmetric fixed point should specify whether this is claimed exactly or only to leading order in 1/N, since the identification of the large-coupling limit with the boundary conditions of Section 5.1.2 is itself made at that order. Finally, the whole of Section 5.3 assumes a cubic coupling of the schematic form (5.8) with the correct parity; the paper acknowledges (Section 3 and footnote 5) that the higher-spin interactions are not written down. The argument should state explicitly which properties of (5.8) are assumed and what would change if the actual N=1 higher-spin interactions did not contain such a term with the required parity.

Minor objections (9)

[Section 4.1, paragraph following Eq. (4.3)] The text reads 'then alpha(-)1(x) represents the one-point function <J(-)1(x)>', but the fields defined in Eq. (4.1) are h(+)1 and h(-)2, so alpha(-)1 is not defined; this should presumably read alpha(+)1. The same sentence should also make clear that the superscript on J refers to parity while the subscript labels the operator, since J(-)1 does not appear elsewhere.
[Eq. (4.4)] Eq. (4.4) is introduced as 'the supersymmetric boundary condition' on the bulk scalars, but Sections 5.1.1 and 5.1.2 exhibit two distinct supersymmetry-preserving choices. The wording should be changed to 'one supersymmetry-preserving boundary condition' or the two choices should be listed here.
[Eq. (5.1) and Section 5.2.2] The statement that the deformation (5.1) is supersymmetric along the line g3 = -2g4 is not derived. A short superfield computation, expanding J^2 in components using (A.8), would let the reader verify the relative coefficient and would also make explicit why the deformation violates parity.
[Section 3, Eq. (3.5) and following text] The notation Phi^a D^{(i1...Di4n)}Phi^a for the higher-spin currents is not standard and the index structure is ambiguous. It would help to write the currents explicitly as symmetrized traceless derivatives, with the spin s indicated, so that the correspondence with the tower in (3.1)-(3.3) can be checked term by term.
[Section 4.2, footnote 4] The formula in footnote 4, '(yD+1/2)K_{1/2}(y)K_{1/2}(y) a-+ = -+ iy gamma^mu n_mu a+-', appears garbled in the present version. It should be restated so that the asymptotic relation (4.18) can be verified independently.
[Appendix A, parity assignments] The parity assignments of the two scalars in the Wess-Zumino multiplet, which are load-bearing for Sections 2 and 5, are supported by a citation to Ref. [26], a 1984 CERN lecture note that is not a published journal article. Either a published reference should be added or the short argument from (A.23) and (A.29) should be spelled out.
[Section 5.3, paragraph containing Eq. (5.10)] The sentence 'Moreover, it is easy to see that when s = 2 the OPE (5.10) is between the same boundary scalar' is unclear as written; the reader cannot tell which two operators are being paired or why this protects the stress tensor. This should be expanded.
[Section 5.2.2 and Section 6] The possibility that (5.1) is exactly marginal is raised and then left open ('it should not be too difficult an issue to settle'). Since this is a concrete, checkable statement about a free CFT, it would be preferable to state it explicitly as a conjecture with the perturbative test that would settle it, rather than as an aside.
[Throughout] There are several typographical errors that should be corrected: 'equivalenty' in Section 5.3, 'the the' in Section 5.2.3 and in the Summary, and 'It is also be of inte rest' in the Summary.

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The paper

The paper claims

A single higher-spin theory on AdS$_4$ is proposed to describe both phases of a three-dimensional supersymmetric vector model.

The reading

The paper proposes that the minimal $N=1$ supersymmetric higher-spin gauge theory on four-dimensional anti-de Sitter space is holographically dual to the singlet sector of the $N=1$ supersymmetric $O(N)$ vector model in three dimensions. The motivation is that a higher-spin bulk carries an infinite tower of massless fields whose boundary counterparts are exactly the conserved currents of a free vector model, so this corner of the AdS/CFT correspondence has a chance to be unusually tractable. The twist is that the same bulk theory appears to describe two boundary theories at once: whether one treats the regular or the irregular falloff of each of the two opposite-parity bulk scalars as the source decides whether the boundary theory sits at the free fixed point or at the strongly coupled one. Parity, rather than the spectrum of dimensions, is what separates the two at large $N$, and the two are related by a Legendre transform. If the proposal holds, one weakly coupled bulk computation would give access to a strongly interacting three-dimensional conformal field theory, and the breaking of higher-spin symmetry at subleading $N$ would be the bulk shadow of anomalous dimensions in the boundary currents.

What carries the argument

The load-bearing device is the pair of admissible quantizations of a conformally coupled AdS$_4$ scalar: its two falloff coefficients $r^{1}$ and $r^{2}$ are related by a kernel that acts as a conformal two-point function, so either coefficient can be chosen as the source and the resulting boundary functionals are Legendre transforms of one another. Combined with the fact that supersymmetry forces the two scalars of the Wess-Zumino multiplet to carry opposite parity, this turns a single bulk theory into two boundary fixed points distinguished only by which parity sits in which quantization slot. The second device is the representation-theoretic statement that a massive spin-$s$ bulk field decomposes as $D(Delta,s) -> D(s+1,s) + D(s+2,s-1)$ as $Delta -> s+1$, which identifies the Goldstone mode that must exist, with the right parity and the right bulk coupling, for a higher-spin field to become massive and for the boundary current to stop being conserved.

Extended reading notes

Core claim

The claim is that the minimal $N=1$ higher-spin theory on AdS$_4$ — built from the two singleton representations $D(1/2,0)$ and $D(1,1/2)$, whose products give one massless $Osp(1|4)$ Wess-Zumino multiplet plus an infinite tower of even-spin fields — is dual to the singlet part of the $N=1$ supersymmetric $O(N)$ vector model in $d=3$. The Wess-Zumino multiplet contains two conformally coupled scalars $h^{(+)}_1$ and $h^{(-)}_2$ of opposite parity and a massless Majorana fermion $PSI$. Choosing the irregular boundary condition for $h^{(+)}_1$ and the regular one for $h^{(-)}_2$, with the matching fermion choice, gives the free $N=1$ supersymmetric $O(N)$ vector model; swapping the two choices gives the strongly coupled fixed point of the same model. At large $N$ the two boundary theories share the same spectrum of operator dimensions and differ only in the parity assignments inside the supermultiplets, which is precisely why a free-field representation of the currents is possible for one and not the other. The paper then argues that at subleading $N$ the boundary conditions selecting the interacting theory cause bulk loops to generate masses for the higher-spin fields, so the corresponding boundary currents acquire order-$1/N$ anomalous dimensions, while the boundary conditions selecting the free theory leave the higher-spin gauge symmetry intact.

Load-bearing premise

The argument assumes that the higher-spin interactions, which the paper does not write down and describes only as computable in principle, preserve the parity assignments and boundary conditions fixed at the quadratic level and include a cubic coupling of the schematic form given in equation (5.8) with the parity needed to generate the loop-induced masses.

Editorial extensions

If this is right

A single bulk higher-spin theory supplies the generating functionals of both the free and the interacting $N=1$ supersymmetric $O(N)$ vector model, with the two related by a Legendre transform rather than by any change in the bulk action.
The free and interacting fixed points are indistinguishable at leading order in $1/N$ by their operator dimensions alone; parity assignments inside the supermultiplets are the only large-$N$ discriminator.
Double-trace deformations of the free boundary theory, including a classically marginal one and a supersymmetry-breaking one, are argued to flow at large coupling and large $N$ back to the same strongly coupled supersymmetric fixed point.
The boundary energy-momentum tensor stays conserved under either choice of boundary conditions, because the operator-product channel that would generate its anomalous dimension cannot supply an operator of the required dimension and parity.
At subleading $N$ only the boundary conditions giving the interacting theory Higgs the higher-spin fields, so the free-theory dual retains its full higher-spin gauge symmetry even after bulk loops are included.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the mechanism is right, it suggests a general diagnostic for higher-spin holography: the pattern of which currents remain exactly conserved at order $1/N$ reads off which quantization of the bulk scalar was chosen, so conservation laws become a probe of boundary conditions rather than of dynamics.
The claim that a supersymmetry-breaking double-trace deformation returns to a supersymmetric fixed point at large $N$ invites a direct perturbative check in the free $O(N)$ vector model, since the deformation is being applied to a free theory where anomalous dimensions and beta functions are computable order by order.
The same Legendre-and-parity structure should apply to the four-dimensional $N=1$ superconformal field theory dual to type IIB on $AdS_5 \times T^{1,1}$, which the paper flags as a place to look for the analogous 'half ultraviolet, half infrared' behaviour.
Away from the large-$N$ limit, the Higgsing picture predicts that the masses generated for higher-spin fields are of order the $1/N$ correction, which would make the higher-spin symmetry an approximate rather than exact feature of the interacting boundary theory.

Original abstract

We argue that the N=1 higher-spin theory on AdS4 is holographically dual to the N=1 supersymmetric critical O(N) vector model in three dimensions. This appears to be a special form of the AdS/CFT correspondence in which both regular and irregular bulk modes have similar roles and their interplay leads simultaneously to both the free and the interacting phases of the boundary theory. We study various boundary conditions that correspond to boundary deformations connecting, for large-N, the free and interacting boundary theories. We point out the importance of parity in this holography and elucidate the Higgs mechanism responsible for the breaking of higher-spin symmetry for subleading N.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.17 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We argue that the N=1 higher-spin theory on AdS4 is holographically dual to the N=1 supersymmetric critical O(N) vector model in three dimensions. This appears to be a special form of the AdS/CFT correspondence in which both regular and irregular bulk modes have similar roles and their interplay leads simultaneously to both the free and the interacting phases of the boundary theory. We study various boundary conditions that correspond to boundary deformations connecting, for large-N, the free and interacting boundary theories. We point out the importance of parity in this holography and elucidate the Higgs mechanism responsible for the breaking of higher-spin symmetry for subleading N.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We argue that the N=1 higher-spin theory on AdS4 is holographically dual to the N=1 supersymmetric critical O(N) vector model in three dimensions.	result 0.71	0.73	0.90	asserted 0.51
s1	This appears to be a special form of the AdS/CFT correspondence in which both regular and irregular bulk modes have similar roles and their interplay leads simultaneously to both the free and the interacting phases of the boundary theory.	interpretation 0.99	0.41	0.13	hedged possibility 0.95
s2	We study various boundary conditions that correspond to boundary deformations connecting, for large-N, the free and interacting boundary theories.	contribution 0.98	0.91	0.06	asserted 0.98
s3	We point out the importance of parity in this holography and elucidate the Higgs mechanism responsible for the breaking of higher-spin symmetry for subleading N.	contribution 0.52	0.87	0.09	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.87 · evidence from argument 0.92.

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sources read

arXiv listing abstract v1

not examined

full text
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references and citing sentences
relations to other papers

levels run

P abstract

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S sections
T body sentences
C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (26)

[4]

I. R. Klebanov and A. M. Polyakov, Phys. Lett. B 550 (2002) 213 [arXiv:hep-th/0210114]

View on Pith Pith review arXiv 2002
[1]

M. A. Vasiliev, Nucl. Phys. B 616 (2001) 106 [Erratum-ibid. B 652 (2003) 407] [arXiv:hep-th/0106200]. M. A. Vasiliev, Phys. Rev. D 66 (2002) 066006 [arXiv:hep-th/0106149]. M. A. Vasiliev, arXiv:hep-th/01 04246. O. V. Shaynkman and M. A. Vasiliev, Theor. Math. Phys. 128 (2001) 1155 [Teor. Mat. Fiz. 128 (2001) 378] [arXiv:hep-th/0103208]. M. A. Vasiliev, ar...

View on Pith Pith review arXiv 2001
[2]

P. Haggi-Mani and B. Sundborg, JHEP 0004 (2000) 031 [arXiv:hep-th/0002189]

View on Pith Pith review arXiv 2000
[3]

M. A. Vasiliev, arXiv:hep-th/0304049. D. Francia and A. Sagnotti, arXiv:hep-th/0212185. J. Engquist, E. Sezgin and P. Sundel l, arXiv:hep-th/0211113. J. Engquist, E. Sezgin and P. Sundell, Class. Quant. Grav. 19 (2002) 6175 [arXiv:hep-th/0207101]. D. Francia and A. Sagnotti, Phys. Lett. B 543 (2002) 303 [arXiv:hep-th/0207002]. E. Sezgin and P. Sundell, Nu...

View on Pith Pith review arXiv 2002
[5]

I. R. Klebanov and E. Witten, Nucl. Phys. B 556 (1999) 89 [arXiv:hep-th/9905104]

View on Pith Pith review arXiv 1999
[6]

S. S. Gubser and I. Mitra, Phys. Rev. D 67, 064018 (2003) [arXiv:hep-th/0210093]

View on Pith Pith review arXiv 2003
[7]

S. S. Gubser and I. R. Klebanov, Nucl. Phys. B 656, 23 (2003) [arXiv:hep-th/0212138]

View on Pith Pith review arXiv 2003
[8]

A. C. Petkou, JHEP 0303 (2003) 049 [arXiv:hep-th/0302063]

View on Pith Pith review arXiv 2003
[9]

A. C. Petkou, Annals Phys. 249 (1996) 180 [arXiv:hep-th/9410093]

View on Pith Pith review arXiv 1996
[10]

J. Zinn-Justin, Nucl. Phys. B 367 (1991) 105

View on Pith 1991
[11]

V. K. Dobrev, Nucl. Phys. B 553 (1999) 559 [arXiv:hep-th/9812194]

View on Pith Pith review arXiv 1999
[12]

K. Koller, Comm. Math. Phys. 40 (1975) 15

View on Pith 1975
[13]

W. Heidenreich, Phys. Lett. B 110 (1982) 461

View on Pith 1982
[14]

W. Muck and K. S. Viswanathan, Phys. Rev. D 60 (1999) 046003 [arXiv:hep-th/9903194]

View on Pith Pith review arXiv 1999
[15]

S. Ferrara and E. Sokatchev, JHEP 0208, 051 (2002) [arXiv:hep-th/0203068]

View on Pith Pith review arXiv 2002
[16]

P. Breitenlohner and D. Z. Freedman, Annals Phys. 144, 249 (1982). – 18 –

View on Pith 1982
[17]

J. A. Gracey, Nucl. Phys. B 348, 737 (1991)

View on Pith 1991
[18]

E. Witten, arXiv:hep-th/0112258

View on Pith Pith review arXiv
[19]

M. Berkooz, A. Sever and A. Shomer, JHEP 0205, 034 (2002) [arXiv:hep-th/0112264]

View on Pith Pith review arXiv 2002
[20]

M. Henneaux, arXiv:hep-th/9902137

View on Pith Pith review arXiv
[21]

V. G. Koures and K. T. Mahanthappa, Phys. Rev. D 45 (1992) 580

View on Pith 1992
[22]

T. Leonhardt, A. Meziane and W. Ruhl, arXiv:hep-th/021 1092

View on Pith
[23]

L. Girardello, M. Porrati and A. Zaﬀaroni, arXiv:hep-th /0212181

View on Pith
[24]

D. Anselmi, Nucl. Phys. B 541 (1999) 323 [arXiv:hep-th/9808004]

View on Pith Pith review arXiv 1999
[25]

I. R. Klebanov and E. Witten, Nucl. Phys. B 536 (1998) 199 [arXiv:hep-th/9807080]

View on Pith Pith review arXiv 1998
[26]

H. Nicolai, CERN-TH-3882 Presented at Spring School on Supergravity and Supersymmetry, Trieste, Italy, Apr 4-14, 1984 – 19 –

View on Pith 1984

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AdS/CFT beyond the unitarity bound
hep-th 2011-05 conditional novelty 7.0 of 10

Conformally invariant (Neumann) boundary conditions for scalars above the Breitenlohner-Freedman window are ghost-free in Poincare AdS, evading unitarity bounds via pure gauge modes and an IR divergence, but ghosts re...
Self-dual holography: four-point AdS/CFT correlators in higher-spin gravity
hep-th 2026-05 unverdicted novelty 6.0 of 10

Develops holographic dictionary for self-dual higher-spin theories and computes four-point AdS/CFT correlators in a higher-spin extension of self-dual Yang-Mills.
$N$-body modelling of the ED-2 stream progenitor shows Gaia BH3's formation involved dynamical interactions
astro-ph.GA 2026-04 unverdicted novelty 6.0 of 10

N-body modeling of the ED-2 progenitor shows Gaia BH3 formed as an exchange binary via multiple dynamical interactions in a dense cluster, not in isolation.
On symmetry breaking in the self-dual higher-spin theory
hep-th 2025-09 conditional novelty 6.0 of 10

In the self-dual higher-spin theory, a scalar vacuum that breaks AdS symmetry to 3D Poincaré makes all higher-spin gauge fields decouple except spin one, and makes higher-spin currents non-conserved except the spin-on...
Higher-spins on Taub-NUT and higher-spin Taub-NUT
hep-th 2025-08 conditional novelty 6.0 of 10

Higher-spin fields are solved exactly on the Taub-NUT instanton in the self-dual Yang-Mills truncation, and an order-by-order convergent higher-spin Taub-NUT solution is constructed in self-dual gravity, organized by ...
Regge trajectories, detectors, and distributions in the critical ${\rm O}(N)$ model
hep-th 2025-06 conditional novelty 6.0 of 10

In the critical O(N) model, renormalizing detector and distribution light-ray operators at leading order in 1/N yields Regge intercepts, the leading-twist splitting function, and a BFKL-type anomalous spin.
Anomalous dimensions at small spins
hep-th 2025-06 accept novelty 6.0 of 10

The quadratic mass-correction combination of twist-two anomalous dimensions stays finite at small spin in the O(N) phi^4, phi^3, and Gross-Neveu-Yukawa models at the computed loop orders, enabling explicit resummations.
Light-Front Bootstrap for Chern-Simons Matter Theories
hep-th 2018-11 conditional novelty 6.0 of 10

Requiring the conformal algebra to close at cubic order in light-cone gauge fixes all three-point functions of higher-spin currents in Chern-Simons matter theories up to two parameters, and produces the cubic higher-s...
Spinning Witten Diagrams
hep-th 2017-02 conditional novelty 6.0 of 10

A systematic framework computes the conformal partial wave expansion of spinning Witten diagrams and reconstructs all cubic couplings of symmetric fields in the dual anti-de Sitter theory.
On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
hep-th 2016-10 accept novelty 6.0 of 10

The paper derives closed-form anomalous dimensions for all higher-spin currents in large-N Chern-Simons scalar and fermion theories, to leading order in 1/N and all orders in the 't Hooft coupling, and checks them aga...
Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
hep-th 2014-10 conditional novelty 6.0 of 10

General formulas for one-loop vacuum energy and conformal anomaly coefficients of arbitrary higher-spin AdS5 fields are derived, and applied to show that each Kaluza-Klein level p of type IIB supergravity on S5 contri...
Higher Spin AdS$_{d+1}$/CFT$_d$ at One Loop
hep-th 2014-01 conditional novelty 6.0 of 10

The regularized one-loop vacuum energy of Vasiliev higher-spin gravity in AdS(d+1) vanishes for all integer spins and equals one real conformal scalar for even spins, in every dimension d >= 2.
Duality in N=2 minimal model holography
hep-th 2012-07 conditional novelty 6.0 of 10

The quantum W-algebra of N=2 higher spin AdS3 gravity depends on one coupling beyond the central charge, and four distinct values of the shs[mu] parameter give the same algebra, proving the bulk and boundary symmetrie...
Scalar fields and three-point functions in D=3 higher spin gravity
hep-th 2011-11 conditional novelty 6.0 of 10

Bulk and boundary computations of scalar-scalar-higher-spin three-point functions in AdS3 higher spin gravity agree exactly for all spins and all values of the deformation parameter.
Higher Spin Gravity with Matter in AdS_3 and Its CFT Dual
hep-th 2011-06 conditional novelty 6.0 of 10

Tree-level three-point functions in Vasiliev higher-spin gravity in AdS3 match the spin-3 current correlator of a subsector of the W_N minimal model at 't Hooft coupling 1/2.
Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings
hep-th 2003-05 conditional novelty 6.0 of 10

The three-scalar amplitude in the Type A higher-spin model vanishes with regular boundary conditions, matching Petkou's O(N) vector-model result and supporting the Klebanov-Polyakov holographic conjecture.
Chiral Higher Spin Gravity in (A)dS${}_4$ and secrets of Chern-Simons Matter Theories
hep-th 2022-05 conditional novelty 5.0 of 10

A local, Lorentz-covariant chiral higher-spin gravity with cosmological constant is constructed as a Free Differential Algebra, smoothly deforming the authors' flat-space construction.
Light-Front Higher-Spin Theories in Flat Space
hep-th 2016-09 conditional novelty 5.0 of 10

Light-cone quantization admits a complete, parity-violating, non-unitary higher-spin theory in four-dimensional flat space whose four-point amplitude vanishes, and it forces every spin to couple to gravity with equal ...
Partition Functions and Casimir Energies in Higher Spin AdS_{d+1}/CFT_d
hep-th 2014-02 conditional novelty 5.0 of 10

The one-loop free energy and Casimir energy of higher-spin gravity in AdS_{d+1} match the order-N^0 terms of large-N singlet-sector free scalar and fermion CFTs on S^1 x S^{d-1} in all dimensions.
F-Theorem without Supersymmetry
hep-th 2011-05 accept novelty 5.0 of 10

The three-sphere free energy decreases along renormalization group flows in a range of non-supersymmetric three-dimensional field theories, consistent with the F-theorem.
On Higher Spin Gauge Theory and the Critical O(N) Model
hep-th 2011-05 conditional novelty 5.0 of 10

The critical O(N) vector model's correlators are shown to follow from the free theory's by flipping the boundary condition on the bulk scalar in Vasiliev's higher-spin gravity, giving a perturbative derivation of the ...
Boundary Conditions and Dualities: Vector Fields in AdS/CFT
hep-th 2006-06 accept novelty 4.5 of 10

For vector fields in AdS, the authors classify allowed boundary conditions and argue that the conjugate choice in AdS4 makes the dual of the bulk photon a dynamical gauge field, with a tensor-field analogue suggesting...
Dirichlet, Neumann, Mixed and self-dual holography: (self-dual) Yang--Mills theory II
hep-th 2026-06 unverdicted novelty 4.0 of 10

Derives bulk and boundary propagators and computes 3- and 4-point correlators for YM, CS and SDYM in AdS/CFT with multiple boundary conditions to relate their observables.
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.
Emergent Spacetime and Holographic CFTs
hep-th 2011-01 conditional novelty 4.0 of 10

Factorization of light-operator correlators requires infinite central charge, and the factorized sector is naturally reorganized as free fields and Witten diagrams in an emergent anti-de Sitter space.
Snowmass White Paper: Higher Spin Gravity and Higher Spin Symmetry
hep-th 2022-05 unverdicted novelty 1.0 of 10

A community survey argues that infinite-dimensional higher spin symmetry may make quantum gravity tractable, and lays out the open problems and mathematical tools of the program.
Black holes in three dimensional higher spin gravity: A review
hep-th 2012-08 accept

The review argues that a holonomy condition on the Chern-Simons connection defines smooth higher spin black holes and yields a generalized Cardy formula that matches CFT at high temperature.

How the literature uses it

77 arXiv papers cite this in 102 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

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Builds on it 1 paper

Further generalizations of the basic dualities discussed so far can be obtained with the help of critical vector models [ref] .

Infinite distances in multicritical CFTs and higher-spin holography · Higher-spin holography · 0.80

Cites it as background 35 papers

The advent of AdS/CFT has revived the interest for these models and in particular for the bosonic one due to its conjectured holographic duality [ref] with the simplest higher-spin gauge theory on AdS$_4$.[For reviews of higher-spin theories see e.g. [ref] .] It was also suggested in [ref] that the fermionic $O(N)$ model also has a higher-spin dual, termed the B-model in [ref] , the latter being the truncation to a conformally coupled pseudoscalar of $N=1$ SUSY higher-spin theory in AdS$_4$.

Singleton deformation of higher-spin theory and the phase structure of the three-dimensional O(N) vector model · Introduction and Summary · 0.89
[Another type of examples are given by Chern-Simons-matter theories in three dimensions [ref] , and the anomalous dimensions of higher spin currents have been computed in [ref] recently.] The model is proposed to be dual to a supersymmetric Vasiliev theory on AdS$_4$ [ref] , and it admits deformations exactly marginal at least to the $1/N$ order.

Marginal deformations of 3d supersymmetric U(N) model and broken higher spin symmetry · Introduction · 0.87
We will concentrate on the higher-spin/vector-model AdS/CFT duality [ref] , although there is also an interesting relation between massless higher spin fields and tensionless strings [ref] with a lot of progress on the string theory side over the last years [ref] .

Infinite distances in multicritical CFTs and higher-spin holography · Introduction · 0.95

Discussion

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[1] [4]

I. R. Klebanov and A. M. Polyakov, Phys. Lett. B 550 (2002) 213 [arXiv:hep-th/0210114]

View on Pith Pith review arXiv 2002

[2] [1]

M. A. Vasiliev, Nucl. Phys. B 616 (2001) 106 [Erratum-ibid. B 652 (2003) 407] [arXiv:hep-th/0106200]. M. A. Vasiliev, Phys. Rev. D 66 (2002) 066006 [arXiv:hep-th/0106149]. M. A. Vasiliev, arXiv:hep-th/01 04246. O. V. Shaynkman and M. A. Vasiliev, Theor. Math. Phys. 128 (2001) 1155 [Teor. Mat. Fiz. 128 (2001) 378] [arXiv:hep-th/0103208]. M. A. Vasiliev, ar...

View on Pith Pith review arXiv 2001

[3] [2]

P. Haggi-Mani and B. Sundborg, JHEP 0004 (2000) 031 [arXiv:hep-th/0002189]

View on Pith Pith review arXiv 2000

[4] [3]

M. A. Vasiliev, arXiv:hep-th/0304049. D. Francia and A. Sagnotti, arXiv:hep-th/0212185. J. Engquist, E. Sezgin and P. Sundel l, arXiv:hep-th/0211113. J. Engquist, E. Sezgin and P. Sundell, Class. Quant. Grav. 19 (2002) 6175 [arXiv:hep-th/0207101]. D. Francia and A. Sagnotti, Phys. Lett. B 543 (2002) 303 [arXiv:hep-th/0207002]. E. Sezgin and P. Sundell, Nu...

View on Pith Pith review arXiv 2002

[5] [5]

I. R. Klebanov and E. Witten, Nucl. Phys. B 556 (1999) 89 [arXiv:hep-th/9905104]

View on Pith Pith review arXiv 1999

[6] [6]

S. S. Gubser and I. Mitra, Phys. Rev. D 67, 064018 (2003) [arXiv:hep-th/0210093]

View on Pith Pith review arXiv 2003

[7] [7]

S. S. Gubser and I. R. Klebanov, Nucl. Phys. B 656, 23 (2003) [arXiv:hep-th/0212138]

View on Pith Pith review arXiv 2003

[8] [8]

A. C. Petkou, JHEP 0303 (2003) 049 [arXiv:hep-th/0302063]

View on Pith Pith review arXiv 2003

[9] [9]

A. C. Petkou, Annals Phys. 249 (1996) 180 [arXiv:hep-th/9410093]

View on Pith Pith review arXiv 1996

[10] [10]

J. Zinn-Justin, Nucl. Phys. B 367 (1991) 105

View on Pith 1991

[11] [11]

V. K. Dobrev, Nucl. Phys. B 553 (1999) 559 [arXiv:hep-th/9812194]

View on Pith Pith review arXiv 1999

[12] [12]

K. Koller, Comm. Math. Phys. 40 (1975) 15

View on Pith 1975

[13] [13]

W. Heidenreich, Phys. Lett. B 110 (1982) 461

View on Pith 1982

[14] [14]

W. Muck and K. S. Viswanathan, Phys. Rev. D 60 (1999) 046003 [arXiv:hep-th/9903194]

View on Pith Pith review arXiv 1999

[15] [15]

S. Ferrara and E. Sokatchev, JHEP 0208, 051 (2002) [arXiv:hep-th/0203068]

View on Pith Pith review arXiv 2002

[16] [16]

P. Breitenlohner and D. Z. Freedman, Annals Phys. 144, 249 (1982). – 18 –

View on Pith 1982

[17] [17]

J. A. Gracey, Nucl. Phys. B 348, 737 (1991)

View on Pith 1991

[18] [18]

E. Witten, arXiv:hep-th/0112258

View on Pith Pith review arXiv

[19] [19]

M. Berkooz, A. Sever and A. Shomer, JHEP 0205, 034 (2002) [arXiv:hep-th/0112264]

View on Pith Pith review arXiv 2002

[20] [20]

M. Henneaux, arXiv:hep-th/9902137

View on Pith Pith review arXiv

[21] [21]

V. G. Koures and K. T. Mahanthappa, Phys. Rev. D 45 (1992) 580

View on Pith 1992

[22] [22]

T. Leonhardt, A. Meziane and W. Ruhl, arXiv:hep-th/021 1092

View on Pith

[23] [23]

L. Girardello, M. Porrati and A. Zaﬀaroni, arXiv:hep-th /0212181

View on Pith

[24] [24]

D. Anselmi, Nucl. Phys. B 541 (1999) 323 [arXiv:hep-th/9808004]

View on Pith Pith review arXiv 1999

[25] [25]

I. R. Klebanov and E. Witten, Nucl. Phys. B 536 (1998) 199 [arXiv:hep-th/9807080]

View on Pith Pith review arXiv 1998

[26] [26]

H. Nicolai, CERN-TH-3882 Presented at Spring School on Supergravity and Supersymmetry, Trieste, Italy, Apr 4-14, 1984 – 19 –

View on Pith 1984