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AdS/CFT for 3D Higher-Spin Gravity Coupled to Matter Fields
High Energy Physics - Theory · Submitted 19 Nov 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim New holographic prescription for the model of 3d higher-spin gravity coupled to real matter fields $B_{\mu\nu}$ and $C$, which was introduced in ArXiv:1304.7941[hep-th], is formulated.
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New holographic prescription for the model of 3d higher-spin gravity coupled to real matter fields $B_{\mu\nu}$ and $C$, which was introduced in ArXiv:1304.7941[hep-th], is formulated. By using a local symmetry, two of the components of $B_{\mu\nu}$ are eliminated, and gauge-fixing conditions are imposed such that the non-vanishing component, $B_{\phi\rho}$, satisfies a covariantly-constancy condition in the background of Chern-Simons gauge fields $A_{\mu}$, $\bar{A}_{\mu}$. In this model, solutions to the classical equations of motion for $A_{\mu}$ and $\bar{A}_{\mu}$ are non-flat due to the interactions with matter fields. The solutions for the gauge fields can, however, be split into two parts, flat gauge fields ${\cal A}_{\mu}$, $\bar{{\cal A}}_{\mu}$, and those terms that depend on the matter fields. The equations for the matter fields then coincide with covariantly-constancy equations in the flat backgrounds ${\cal A}_{\mu}$ and $\bar{{\cal A}}_{\mu}$, which are exactly the same as those in linearized 3d Vasiliev gravity. The two- and three-point correlation functions of operators in the boundary CFT are computed by using an on-shell action, $ \text{tr}\, (B_{\phi\rho} \, C)$. This term does not depend on coordinates due to the matter equations of motion, and it is not necessary to take the near-boundary limit $\rho \rightarrow \infty$. Analysis is presented for SL(3,R) $\times$ SL(3,R) as well as $HS[\frac{1}{2}] \times HS[\frac{1}{2}]$ higher-spin gravity. In the latter model, scalar operators with scaling dimensions $\Delta_+=\frac{3}{2}$ and $\Delta_-=\frac{1}{2}$ appear in a single quantization.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | New holographic prescription for the model of 3d higher-spin gravity coupled to real matter fields $B_{\mu\nu}$ and $C$, which was introduced in ArXiv:1304.7941[hep-th], is formulated. | contribution 0.99 | 0.85 | 0.23 | asserted 1.00 |
| s1 | By using a local symmetry, two of the components of $B_{\mu\nu}$ are eliminated, and gauge-fixing conditions are imposed such that the non-vanishing component, $B_{\phi\rho}$, satisfies a covariantly-constancy condition in the background of Chern-Simons gauge fields $A_{\mu}$, $\bar{A}_{\mu}$. | method 0.98 | 0.78 | 0.06 | asserted 1.00 |
| s2 | In this model, solutions to the classical equations of motion for $A_{\mu}$ and $\bar{A}_{\mu}$ are non-flat due to the interactions with matter fields. | result 0.85 | 0.55 | 0.07 | asserted 1.00 |
| s3 | The solutions for the gauge fields can, however, be split into two parts, flat gauge fields ${\cal A}_{\mu}$, $\bar{{\cal A}}_{\mu}$, and those terms that depend on the matter fields. | method 0.63 | 0.74 | 0.09 | asserted 0.60 |
| s4 | The equations for the matter fields then coincide with covariantly-constancy equations in the flat backgrounds ${\cal A}_{\mu}$ and $\bar{{\cal A}}_{\mu}$, which are exactly the same as those in linearized 3d Vasiliev gravity. | result 0.83 | 0.73 | 0.23 | asserted 1.00 |
| s5 | The two- and three-point correlation functions of operators in the boundary CFT are computed by using an on-shell action, $ \text{tr}\, (B_{\phi\rho} \, C)$. | method 0.68 | 0.90 | 0.16 | asserted 1.00 |
| s6 | This term does not depend on coordinates due to the matter equations of motion, and it is not necessary to take the near-boundary limit $\rho \rightarrow \infty$. | result 0.50 | 0.85 | 0.08 | asserted 1.00 |
| s7 | Analysis is presented for SL(3,R) $\times$ SL(3,R) as well as $HS[\frac{1}{2}] \times HS[\frac{1}{2}]$ higher-spin gravity. | contribution 0.93 | 0.80 | 0.05 | asserted 0.97 |
| s8 | In the latter model, scalar operators with scaling dimensions $\Delta_+=\frac{3}{2}$ and $\Delta_-=\frac{1}{2}$ appear in a single quantization. | result 0.95 | 0.73 | 0.09 | asserted 1.00 |
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Original abstract
New holographic prescription for the model of 3d higher-spin gravity coupled to real matter fields $B_{\mu\nu}$ and $C$, which was introduced in ArXiv:1304.7941[hep-th], is formulated. By using a local symmetry, two of the components of $B_{\mu\nu}$ are eliminated, and gauge-fixing conditions are imposed such that the non-vanishing component, $B_{\phi\rho}$, satisfies a covariantly-constancy condition in the background of Chern-Simons gauge fields $A_{\mu}$, $\bar{A}_{\mu}$. In this model, solutions to the classical equations of motion for $A_{\mu}$ and $\bar{A}_{\mu}$ are non-flat due to the interactions with matter fields. The solutions for the gauge fields can, however, be split into two parts, flat gauge fields ${\cal A}_{\mu}$, $\bar{{\cal A}}_{\mu}$, and those terms that depend on the matter fields. The equations for the matter fields then coincide with covariantly-constancy equations in the flat backgrounds ${\cal A}_{\mu}$ and $\bar{{\cal A}}_{\mu}$, which are exactly the same as those in linearized 3d Vasiliev gravity. The two- and three-point correlation functions of operators in the boundary CFT are computed by using an on-shell action, $ \text{tr}\, (B_{\phi\rho} \, C)$. This term does not depend on coordinates due to the matter equations of motion, and it is not necessary to take the near-boundary limit $\rho \rightarrow \infty$. Analysis is presented for SL(3,R) $\times$ SL(3,R) as well as $HS[\frac{1}{2}] \times HS[\frac{1}{2}]$ higher-spin gravity. In the latter model, scalar operators with scaling dimensions $\Delta_+=\frac{3}{2}$ and $\Delta_-=\frac{1}{2}$ appear in a single quantization.
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References
How the literature uses it
10 arXiv papers cite this in 17 sentences
Papers citing it · 10 sentences without a confident label
Compares with it 2 papers
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The field equations of the HS field resemble the form of the matter field equations introduced in [ref] .
Generalized Chern-Simons higher-spin gravity theories in three dimensions · Conclusions · 0.97
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E2 is formally equivalent to the Cartan integrability of the equations of motion of the three-dimensional matter-coupled higher spin gravities proposed in [ref] . ]
4D Higher Spin Gravity with Dynamical Two-Form as a Frobenius--Chern--Simons Gauge Theory · Component formulation · 0.96
Cites it as background 4 papers
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In the above works, the (classical) gauge sector is assumed to be described by various CS generalisations [ref] of the Achucarro–Townsend supergravity Lagrangian [ref] .
An Action for Matter Coupled Higher Spin Gravity in Three Dimensions · Introduction · 0.98
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Various ramifications of it introduced more complex dynamics both in terms of the geometric content such as e.g. adding a gravitational Chern–Simons (CS) term [ref] or other higher derivative interactions [ref] , inclusion of matter interactions [ref] as well as varied boundary conditions [ref] .
Spectral Flow in 3D Flat Spacetimes · Introduction · 0.91
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Subsequently extensive analyses have been done for the $W_N$ minimal conformal field theories and many evidences are presented for the relevance of the higher spin field theories together with gravity for these minimal models in the large $N$ limit [ref] .
Ising Model on Twisted Lattice and Holographic RG flow · Introduction · 0.89
What it cites · 18 sentences without a confident label
Compares with 2 papers
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In the usual AdS/CFT correspondence of the scalar field [ref] [ref] , only operator $O^(1,1)$ can be considered in the standard quantization, and only $O^(0,0)$ in the alternate quantization.
Anti De Sitter Space And Holography · Primary Operators · 0.85
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Comparing this with the result of [ref] , $Δ=d/2+m$ with $d=2$, we again find that the fermion is massless, $m=0$.
Spinors and the AdS/CFT correspondence · Primary Operators · 0.96
Cites as background 24 papers
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In this section we will review the model of 3d higher spin gravity coupled to matter fields, which was introduced in [ref] .
Metric-Like Formalism for Matter Fields Coupled to 3D Higher Spin Gravity · Model · 0.89
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This model is defined by an action integral $S_CS-BC=S_CS+S_BC$, where $S_CS$ is Chern-Simons (CS) action [ref] [equation] Here $M=ℝ ×Σ$ is a 3d manifold and $Σ$ is a 2d manifold with boundary $∂ Σ≅S^1$.
Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields · Model · 0.87
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[ref] [ref] [ref] [ref] [ref] Asymptotic symmetry algebra of 3d higher-spin gravity is discussed in [ref] , [ref] .
Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity · Introduction · 0.98
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