Semi-classical unitarity in 3-dimensional higher-spin gravity for non-principal embeddings

D. Grumiller; H. Afshar; M. Gary; M. Riegler; R. Rashkov

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Semi-classical unitarity in 3-dimensional higher-spin gravity for non-principal embeddings

H. Afshar, M. Gary, D. Grumiller, R. Rashkov, M. Riegler

High Energy Physics - Theory · Submitted 19 Nov 2012

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

The authors' main claim Based upon the Feigin-Semikhatov generalization of the Polyakov-Bershadsky algebra, we construct infinite families of unitary higher-spin gravity theories at certain rational values of the Chern-Simons level that allow arbitrarily large values of the central charge up to c = N/4 - 1/8 - O(1/N), thereby confirming a recent speculation by us 1209.2860.

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arXiv ID1211.4454 (version 2)

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CitationD. Grumiller, H. Afshar, M. Gary, M. Riegler, R. Rashkov. "Semi-classical unitarity in 3-dimensional higher-spin gravity for non-principal embeddings." arXiv:1211.4454 (2012). https://pith.science/paper/FYHQX43N

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What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.53 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.93 · mentions code or data availability 0.02.

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Higher-spin gravity in three dimensions is efficiently formulated as a Chern-Simons gauge-theory, typically with gauge algebra sl(N)+sl(N). The classical and quantum properties of the higher-spin theory depend crucially on the embedding into the full gauge algebra of the sl(2)+sl(2) factor associated with gravity. It has been argued previously that non-principal embeddings do not allow for a semi-classical limit (large values of the central charge) consistent with unitarity. In this work we show that it is possible to circumvent these conclusions. Based upon the Feigin-Semikhatov generalization of the Polyakov-Bershadsky algebra, we construct infinite families of unitary higher-spin gravity theories at certain rational values of the Chern-Simons level that allow arbitrarily large values of the central charge up to c = N/4 - 1/8 - O(1/N), thereby confirming a recent speculation by us 1209.2860.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Higher-spin gravity in three dimensions is efficiently formulated as a Chern-Simons gauge-theory, typically with gauge algebra sl(N)+sl(N).	background 1.00	0.05	0.02	asserted 0.96
s1	The classical and quantum properties of the higher-spin theory depend crucially on the embedding into the full gauge algebra of the sl(2)+sl(2) factor associated with gravity.	background 1.00	0.05	0.02	asserted 0.99
s2	It has been argued previously that non-principal embeddings do not allow for a semi-classical limit (large values of the central charge) consistent with unitarity.	background 0.93	0.03	0.03	asserted 0.60
s3	In this work we show that it is possible to circumvent these conclusions.	contribution 0.79	0.83	0.30	asserted 0.85
s4	Based upon the Feigin-Semikhatov generalization of the Polyakov-Bershadsky algebra, we construct infinite families of unitary higher-spin gravity theories at certain rational values of the Chern-Simons level that allow arbitrarily large values of the central charge up to c = N/4 - 1/8 - O(1/N), thereby confirming a recent speculation by us 1209.2860.	result 0.70	0.95	0.92	asserted 1.00

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Original abstract

Higher-spin gravity in three dimensions is efficiently formulated as a Chern-Simons gauge-theory, typically with gauge algebra sl(N)+sl(N). The classical and quantum properties of the higher-spin theory depend crucially on the embedding into the full gauge algebra of the sl(2)+sl(2) factor associated with gravity. It has been argued previously that non-principal embeddings do not allow for a semi-classical limit (large values of the central charge) consistent with unitarity. In this work we show that it is possible to circumvent these conclusions. Based upon the Feigin-Semikhatov generalization of the Polyakov-Bershadsky algebra, we construct infinite families of unitary higher-spin gravity theories at certain rational values of the Chern-Simons level that allow arbitrarily large values of the central charge up to c = N/4 - 1/8 - O(1/N), thereby confirming a recent speculation by us 1209.2860.

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Cited by 5 Pith papers

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

Generalized Black Holes in Three-dimensional Spacetime
hep-th 2014-04 accept novelty 7.0 of 10

The first proposed higher-spin black hole in 2+1 dimensions is reclassified as a lower-spin solution, and a genuine higher-spin black hole with W_3 asymptotics is constructed.
Flat space (higher spin) gravity with chemical potentials
hep-th 2014-11 conditional novelty 6.0 of 10

Flat space spin-3 gravity with chemical potentials yields an explicit entropy formula for flat space cosmologies and reveals first-order phase transitions that do not appear in the anti-de Sitter case.
Enhanced asymptotic symmetry algebra of AdS3
hep-th 2013-03 accept novelty 6.0 of 10

Fixing only the conformal structure of the boundary metric in three-dimensional gravity yields an enlarged asymptotic symmetry algebra with two Virasoro algebras, two U(1) currents, and a new central charge k = -l/(8G).
Unitary quantum conformal Bondi-Metzner-Sachs field theories
hep-th 2026-09 conditional novelty 5.0 of 10

Unitarity restricts the central charge of conformal BMS3 field theories to four discrete values: 1, 3/2, 13/7, and 2, with explicit spectra of primaries given for each.
Holographic applications of logarithmic conformal field theories
hep-th 2013-02 accept novelty 3.0 of 10

Critically tuned anti-de Sitter gravity theories are conjectured to be dual to logarithmic conformal field theories, and this review assembles the correlator and partition-function evidence for that correspondence.

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17 arXiv papers cite this in 26 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 a conflicting result 1 paper

A simple inspection of these algebras indicates that only the W_N algebra constructed using the principal embedding could admit a unitary representation for large values of the central charge.

Unitarity Bounds in AdS_3 Higher Spin Gravity · 0.99

Papers citing it · 19 sentences without a confident label

Builds on it 1 paper

Besides, the argument to circumvent this non-unitarity in [ref] may be extended to the supersymmetric case as well.

Dualities from higher-spin supergravity · A remark on the central charge · 0.99

Uses its method or tool 1 paper

For the sake of completeness, we outline the procedure determining the asymptotic symmetry algebra for the AdS background represented by eq.[ref], following the general idea in [ref] (see also [ref] ).

Asymptotic symmetries and thermodynamics of higher spin black holes in AdS3 · Asymptotic algebra for the $(2,1,1)$ embedding · 0.93

Compares with it 2 papers

The algebra agrees with the semiclassical limit of the result quoted in [ref] .

Asymptotic symmetries and thermodynamics of higher spin black holes in AdS3 · Asymptotic algebra for the $(2,1,1)$ embedding · 0.99
Similar behavior has been encountered in other holographic settings [ref] .] The “offensive,” and apparently worrisome, relation can be tracked back to the mode $A^(2)$ in [ref] (or $∂_+ P$ in 3D variables).

Comments on AdS_2 Gravity · Higher dimensional perspective: gluing negative energy photons · 0.88

Cites it as background 3 papers

Let us also mention that analogous issues in the higher-spin context and in a wider class of examples have been discussed in [ref] and [ref] , respectively.

Asymptotic Symmetries of Colored Gravity in Three Dimensions · Discussions · 0.90
Moreover, we focused exclusively on the principal embedding of $sl(2,ℝ)$ into $sl(N,ℝ)$ [ref] .

Higher Spin Black Holes with Soft Hair · Discussion · 0.89
See [ref] for recent work on such theories.

A note on interface solutions in higher-spin gravity · Introduction · 0.98

What it cites · 25 sentences without a confident label

Builds on 1 paper

It would be interesting to generalize the discussion of [ref] to $W_N^(2)$ gravity to verify how many of such models survive these checks.

The Gravity Dual of the Ising Model · Conclusions · 0.88

Uses the method or tool of 1 paper

Following the algorithm outlined in [ref] with the boundary conditions above leads to the $W_N^(2)$ algebra discussed in section [ref] times another $û(1)$ current algebra with level $κ$ [ref] as quantum ASA.

Non-AdS holography in 3-dimensional higher spin gravity - General recipe and example · AdS and Lobachevsky boundary conditions · 0.82

Compares with 1 paper

This is quite different from the situation encountered in [ref] .

The Gravity Dual of the Ising Model · AdS and Lobachevsky boundary conditions · 1.00

Cites as background 35 papers

We review now the most relevant aspects of the algebra $W_N^(2)$ [ref] , which depends on the parameter $N$ and a level $k$ [not to be confused with the Chern–Simons level in [ref]].

$W^{(2)}_n$ algebras · $W_N^(2)$ gravity · 0.95
While it cannot be ruled out that dropping this assumption leads to a satisfactory family of quantum gravity models (for instance in the context of minimal model holography [ref] ), it is much harder to study such models on the gravity side.

Minimal Model Holography · Introduction · 0.92
While it cannot be ruled out that dropping this assumption leads to a satisfactory family of quantum gravity models (for instance in the context of minimal model holography [ref] ), it is much harder to study such models on the gravity side.

An AdS_3 Dual for Minimal Model CFTs · Introduction · 0.92

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