On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory

doi:10.1088/1126-6708/2008/08/056

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On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory

Journal Article•DOI•

On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory

Nicolas Boulanger¹, Per Sundell, Serge Leclercq²•Institutions (2)

Scuola Normale Superiore di Pisa¹, University of Mons²

01 Aug 2008-Journal of High Energy Physics (Springer Verlag)-Vol. 2008, Iss: 8, pp 056-056

TL;DR: In this paper, the uniqueness of the minimal couplings between higher-spin fields and gravity has been studied in the context of higher spin field equations with ε > 0 and ε = 3.

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Abstract: We address the uniqueness of the minimal couplings between higher-spin fields and gravity. These couplings are cubic vertices built from gauge non-invariant connections that induce non-abelian deformations of the gauge algebra. We show that Fradkin-Vasiliev's cubic 2?s?s vertex, which contains up to 2s?2 derivatives dressed by a cosmological constant ?, has a limit where: (i) ????0; (ii) the spin-2 Weyl tensor scales non-uniformly with s; and (iii) all lower-derivative couplings are scaled away. For s = 3 the limit yields the unique non-abelian spin 2?3?3 vertex found recently by two of the authors, thereby proving the uniqueness of the corresponding FV vertex. We extend the analysis to s = 4 and a class of spin 1?s?s vertices. The non-universality of the flat limit high-lightens not only the problematic aspects of higher-spin interactions with ? = 0 but also the strongly coupled nature of the derivative expansion of the fully nonlinear higher-spin field equations with ??0, wherein the standard minimal couplings mediated via the Lorentz connection are subleading at energy scales (|?|)1/2??E??Mp. Finally, combining our results with those obtained by Metsaev, we give the complete list of all the manifestly covariant cubic couplings of the form 1?s?s? and 2?s?s?, in Minkowski background.

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Journal Article•DOI•

How higher-spin gravity surpasses the spin-two barrier

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Xavier Bekaert¹, Nicolas Boulanger², Per Sundell•Institutions (2)

François Rabelais University¹, University of Mons²

03 Jul 2012-Reviews of Modern Physics

TL;DR: In this paper, the key mechanisms of higher-spin extensions of ordinary gravities in four dimensions and higher are explained, and an overview of various no-go theorems for low-energy scattering of massless particles in flat spacetime is given.

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Abstract: Aiming at nonexperts, the key mechanisms of higher-spin extensions of ordinary gravities in four dimensions and higher are explained. An overview of various no-go theorems for low-energy scattering of massless particles in flat spacetime is given. In doing so, a connection between the $S$-matrix and the Lagrangian approaches is made, exhibiting their relative advantages and weaknesses, after which potential loopholes for nontrivial massless dynamics are highlighted. Positive yes-go results for non-Abelian cubic higher-derivative vertices in constantly curved backgrounds are reviewed. Finally, how higher-spin symmetry can be reconciled with the equivalence principle in the presence of a cosmological constant leading to the Fradkin-Vasiliev vertices and Vasiliev's higher-spin gravity with its double perturbative expansion (in terms of numbers of fields and derivatives) is outlined.

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383 citations

Cites background or methods from "On The Uniqueness of Minimal Coupli..."

...As was demonstrated in [28], in a flat background the non-abelian 2-s-s vertex is unique and involves a total number of 2s−2 derivatives....
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...Recently, motivated by the similarities between open string theory and higher-spin gravities mainly at the level free fields [24, 25], Sagnotti and Taronna [26] have deconstructed its first Regge trajectory and arrived at the germs of the non-abelian interactions for massless totally symmetric tensors in flat spacetime [27, 28] whose deformations into (A)dS spacetimes [28] lead to the Fradkin–Vasiliev cubic vertices....
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...Therefore (Weinberg’s equivalence principle) all particles interacting with low-spin particles must also couple minimally to the graviton at low energy, but (generalized Weinberg–Witten theorem [43] and identical results presented in [58, 28]) massless higher-spin particles cannot couple minimally to gravity around the flat background....
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...He has also managed to show [30] that these higher-spin states interact with the closed-string graviton and that these interaction reproduce the aforementioned germs of [27, 28]....
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...The complete no-go result ruling out the Lorentz minimal coupling of type 2-s-s in the Lagrangian approach is given in [28]....
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Journal Article•DOI•

Higher spin realization of the DS/CFT correspondence

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Dionysios Anninos, Thomas Hartman, Andrew Strominger

05 Jan 2017-Classical and Quantum Gravity

TL;DR: In this article, the authors conjecture that Vasiliev's theory of higher spin gravity in four-dimensional de Sitter space is holographically dual to a three-dimensional conformal field theory (CFT(3)) living on the spacelike boundary of dS(4) at future timelike infinity.

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Abstract: We conjecture that Vasiliev’s theory of higher spin gravity in four-dimensional de Sitter space (dS(4)) is holographically dual to a three-dimensional conformal field theory (CFT(3)) living on the spacelike boundary of dS(4) at future timelike infinity. The CFT(3) is the Euclidean Sp(N) vector model with anticommuting scalars. The free CFT(3) flows under a double-trace deformation to an interacting CFT(3) in the IR. We argue that both CFTs are dual to Vasiliev dS(4) gravity but with different future boundary conditions on the bulk scalar field. Our analysis rests heavily on analytic continuations of bulk and boundary correlators in the proposed duality relating the O(N) model with Vasiliev gravity in AdS(4).

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310 citations

Journal Article•DOI•

String Lessons for Higher-Spin Interactions

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Augusto Sagnotti, Massimo Taronna

21 Jan 2011-Nuclear Physics

TL;DR: In this paper, a simplified form for the three-point (and four-point) amplitudes of the symmetric tensors belonging to the first Regge trajectory of the open bosonic string is presented.

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267 citations

Posted Content•

Higher Spin Realization of the dS/CFT Correspondence

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Dionysios Anninos, Thomas Hartman, Andrew Strominger

29 Aug 2011-arXiv: High Energy Physics - Theory

TL;DR: In this article, the authors conjecture that Vasiliev's theory of higher spin gravity in four-dimensional de Sitter space (dS) is holographically dual to a three-dimensional conformal field theory (CFT) living on the spacelike boundary of dS at future timelike infinity.

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Abstract: We conjecture that Vasiliev's theory of higher spin gravity in four-dimensional de Sitter space (dS) is holographically dual to a three-dimensional conformal field theory (CFT) living on the spacelike boundary of dS at future timelike infinity. The CFT is the Euclidean Sp(N) vector model with anticommuting scalars. The free CFT flows under a double-trace deformation to an interacting CFT in the IR. We argue that both CFTs are dual to Vasiliev dS gravity but with different future boundary conditions on the bulk scalar field. Our analysis rests heavily on analytic continuations of bulk and boundary correlators in the proposed duality relating the O(N) model with Vasiliev gravity in AdS.

...read moreread less

241 citations

Cites background from "On The Uniqueness of Minimal Coupli..."

...For example, cubic interactions among spins (2, s, s) involving the spin 2 metric fluctuation h given explicitly in [46, 47] take the schematic form...
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Journal Article•DOI•

Quartic AdS interactions in higher-spin gravity from Conformal Field Theory

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Xavier Bekaert¹, Johanna Erdmenger², Dmitry Ponomarev³, Charlotte Sleight²•Institutions (3)

François Rabelais University¹, Max Planck Society², Ludwig Maximilian University of Munich³

18 Aug 2015-Journal of High Energy Physics

TL;DR: In this paper, the quartic vertex is obtained from the field theory four-point function of the operator dual to the bulk scalar, by making use of previous results for the Witten diagrams of higher-spin exchanges.

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Abstract: Clarifying the locality properties of higher-spin gravity is a pressing task, but notoriously difficult due to the absence of a weakly-coupled flat regime. The simplest non-trivial case where this question can be addressed is the quartic self-interaction of the AdS scalar field present in the higher-spin multiplet. We investigate this issue in the context of the holographic duality between the minimal bosonic higher-spin theory on AdS4 and the free O(N) vector model in three dimensions. In particular, we determine the exact explicit form of the derivative expansion of the bulk scalar quartic vertex. The quartic vertex is obtained from the field theory four-point function of the operator dual to the bulk scalar, by making use of our previous results for the Witten diagrams of higher-spin exchanges. This is facilitated by establishing the conformal block expansions of both the boundary four-point function and the dual bulk Witten diagram amplitudes. We show that the vertex we find satisfies a generalised notion of locality.

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220 citations

Cites background from "On The Uniqueness of Minimal Coupli..."

...For these vertices, what remains in the flat space limit is only the term with the highest number of derivatives [8, 15]....
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References

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Quantization of Gauge Systems

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Marc Henneaux, Claudio Teitelboim

08 Nov 1992

TL;DR: In this paper, a systematic study of the classical and quantum theories of gauge systems is presented, starting with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems, and the classical foundations of BRST theory are laid out with a review of the necessary concepts from homological algebra.

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Abstract: This is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical foundations of BRST theory are then laid out with a review of the necessary concepts from homological algebra. Reducible gauge systems are discussed, and the relationship between BRST cohomology and gauge invariance is carefully explained. The authors then proceed to the canonical quantization of gauge systems, first without ghosts (reduced phase space quantization, Dirac method) and second in the BRST context (quantum BRST cohomology). The path integral is discussed next. The analysis covers indefinite metric systems, operator insertions and Ward identities. The antifield formalism is also studied and its equivalence with canonical methods is derived. The examples of electromagnetism and Abelian 2-form gauge fields are treated in detail. The book gives a general and unified treatment of the subject in a self-contained manner. Exercises are provided at the end of each chapter, and pedagogical examples are covered in the text.

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3,520 citations

"On The Uniqueness of Minimal Coupli..." refers background in this paper

...ﬁnition is appropriate for both functionals and diﬀerentials forms. In the former case, the summation over Ialso implies an integration over spacetime (de Witt’s condensed notation). See the textbook [36] for a thorough exposition of the BRST formalism. The action of the BRST diﬀerential sis deﬁned by sA= (W0 ,A) . The diﬀerential sis the sum of the Koszul-Tate diﬀerential δ(which reproduces the equat...
[...]

Posted Content•

New features of FORM

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Jos Vermaseren

19 Oct 2000-arXiv: Mathematical Physics

TL;DR: Forms 3 as mentioned in this paper contains many new features that are inspired by current developments in the methodology of computations in quantum field theory A number of these features are discussed in combination with examples In addition the distribution contains a number of general purpose packages These are described shortly

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Abstract: Version 3 of FORM is introduced It contains many new features that are inspired by current developments in the methodology of computations in quantum field theory A number of these features is discussed in combination with examples In addition the distribution contains a number of general purpose packages These are described shortly

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1,279 citations

"On The Uniqueness of Minimal Coupli..." refers methods in this paper

...By using the software FORM [40], we managed to solve the heavy system of equations and found a consistent set of coefficients....
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Journal Article•DOI•

Nonlinear equations for symmetric massless higher spin fields in (A)dSd

[...]

Mikhail A. Vasiliev¹•Institutions (1)

Lebedev Physical Institute¹

07 Aug 2003-Physics Letters B

TL;DR: In this article, nonlinear field equations for totally symmetric bosonic massless fields of all spins in any dimension are presented, and a nonlinear nonlinear model of the field equations is proposed.

...read moreread less

756 citations

"On The Uniqueness of Minimal Coupli..." refers background in this paper

...Thanks to Vasiliev’s oscillator constructions [20, 21] it has been established that fully nonlinear nonabelian higher-spin gauge field equations exist in arbitrary dimensions in the case of symmetric rank-s tensor gauge fields....
[...]

Journal Article•DOI•

Consistent equations for interacting gauge fields of all spins in 3+1 dimensions

[...]

Mikhail A. Vasiliev¹•Institutions (1)

Lebedev Physical Institute¹

05 Jul 1990-Physics Letters B

TL;DR: In this paper, consistent equations of motion of interacting gauge fields of all spins in 3+1 dimensions are formulated in a closed form, which are explicitly general coordinate invariant, possess all necessary higher spin gauge symmetries and reduce to the usual equations of free massless fields at the linearized level.

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754 citations

"On The Uniqueness of Minimal Coupli..." refers background in this paper

...Thanks to Vasiliev’s oscillator constructions [20, 21] it has been established that fully nonlinear nonabelian higher-spin gauge field equations exist in arbitrary dimensions in the case of symmetric rank-s tensor gauge fields....
[...]

Journal Article•DOI•

On the Gravitational Interaction of Massless Higher Spin Fields

[...]

E.S. Fradkin¹, Mikhail A. Vasiliev¹•Institutions (1)

Lebedev Physical Institute¹

30 Apr 1987-Physics Letters B

TL;DR: In this article, it was shown that the gravitational interaction of massless higher-spin fields (s > 2) does exist at least in the first nontrivial order, despite a widespread belief.

...read moreread less

574 citations

"On The Uniqueness of Minimal Coupli..." refers background or methods in this paper

...One of these two candidates has 2s − 3 derivatives and must therefore give rise to a vertex with 2s − 2 derivatives to be identified with the flat limit of the corresponding FV 2 − s − s top vertex [11, 12]....
[...]
...In the same section 5, combining the cohomological approach with the lightcone results of Metsaev [4, 5], we show that there exists only one nonabelian 2−s−s coupling, which contains 2s − 2 derivatives and must be the flat limit of the well-known nonabelian Fradkin–Vasiliev vertex [11, 12] in AdS , as we verify explicitly for s = 3....
[...]
...Again, by the uniqueness of the nonabelian vertex, we know that it is the flat limit of the corresponding AdS Fradkin–Vasiliev (FV) vertex [11, 12]....
[...]