On nonlinear higher spin curvature

Manvelyan, Ruben; Mkrtchyan, Karapet; Rühl, W.; Tovmasyan, Murad

doi:10.1016/j.physletb.2011.03.069

Cited by 19 publications

(11 citation statements)

References 40 publications

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“…We hope that the results of this paper provide a good piece of illustration of the efficiency of the frame-like and unfolded formalisms that operate with well-organized sets of fields associated with the HS algebra. Of course, the metric-like formulation should also be well organized in terms of the corresponding geometric structures found for free fields in [86] (see also [87,88,89]) provided that their non-Abelian extension explored recently in [90] is available. However, as Cartan geometry contains the Riemann one, the non-linear HS curvatures in the frame-like formalism will reproduce those of the metric-like.…”

Section: Resultsmentioning

confidence: 99%

Cubic vertices for symmetric higher-spin gauge fields in

2012

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Cubic vertices for symmetric higher-spin gauge fields of integer spins in (A)dS d are analyzed. (A)dS d generalization of the previously known action in AdS 4 , that describes cubic interactions of symmetric massless fields of all integer spins s ≥ 2, is found. A new cohomological formalism for the analysis of vertices of higher-spin fields of any symmetry and/or order of nonlinearity is proposed within the frame-like approach. Using examples of spins two and three it is demonstrated how nontrivial vertices in (A)dS d , including Einstein cubic vertex, can result from the AdS deformation of trivial Minkowski vertices. A set of higher-derivative cubic vertices for any three bosonic fields of spins s ≥ 2 is proposed, which is conjectured to describe all vertices in AdS d that can be constructed in terms of connection one-forms and curvature two-forms of symmetric higher-spin fields. A problem of reconstruction of a full nonlinear action starting from known unfolded equations is discussed. It is shown that the normalization of free higher-spin gauge fields compatible with the flat limit relates the noncommutativity parameter of the higher-spin algebra to the (A)dS radius. 10 Towards full nonlinear action 66 11 Conclusion 69 Appendix A. Frame-like derivation of the BBD vertex 71 Appendix B. On-shell identities 72 References 73

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Section: Resultsmentioning

confidence: 99%

Cubic vertices for symmetric higher-spin gauge fields in

2012

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“…The higher-spin curvatures of [34,33,26] provide a long-recognized elegant structure, more recently shown to be capable of encoding all relevant information concerning free higherspin dynamics. However, their remarkable algebraic properties notwithstanding, the role of metric-like higher-spin curvatures in clarifying features of higher-spin interactions is at present little explored -aside from the trivial possibility of making use of them to define abelian-invariant vertices [36]-while their non-linear deformations are known only up to the quadratic contribution computed in [37]. It is anyway noteworthy that one can formulate high-derivative equations propagating only the modes of the two-derivative equations defined in (1.1) and (1.2).…”

Section: Discussionmentioning

confidence: 99%

Generalized connections and higher spin equations

Francia

2012

Class. Quantum Grav.

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We consider high-derivative equations obtained setting to zero the divergence of the higher-spin curvatures in metric-like form, showing their equivalence to the second-order equations emerging from the tensionless limit of open string field theory, which propagate reducible spectra of particles with different spins. This result can be viewed as complementary to the possibility of setting to zero a single trace of the higher-spin field strengths, which yields an equation known to imply Fronsdal's equation in the compensator form. Higher traces and divergences of the curvatures produce a whole pattern of high-derivative equations whose systematics is also presented.

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“…19 See [78] for an analysis of flat-space gauge algebras. 20 See [21,22] for the free HS geometric equations, and [79] for a recent development on HS curvatures. 21 See [80,81] for the recent development of the free massive HS theory in the metric-like approach.…”

Section: A Foregoing the Traceless And Transverse Constraintsmentioning

confidence: 99%

Cubic interactions of massless higher spins in (A)dS: Metric-like approach

2012

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Cubic interactions of higher-spin gauge fields in (A)dS d are studied in the metric-like approach. Making use of the traceless and transverse constraints together with the ambient-space formalism, all consistent parity-invariant cubic vertices are obtained for d ≥ 4 in a closed form pointing out the key role of their flat-space counterparts. IntroductionUnderstanding the systematics of higher-spin (HS) gauge theories 1 has been attracting an increasing attention in recent years, and finding a consistent Lagrangian that describes their interactions is one of the main problems in the subject. Vasiliev's equations [10,11] provide at present the only known fully non-linear consistent description, at least at the classical level, of an infinite number of HS gauge fields of all spins. 2 However the nature of their couplings still leaves interesting questions to be answered. The generalization of the lower-spin gauge interactions of Yang-Mills and Gravity to HS is associated with a non-linear deformation of the Abelian HS gauge symmetries of the free theory [19,20] 3 and can be studied perturbatively by means of the Noether procedure. This actually rests on enforcing gauge invariance of the full Lagrangian order by order in the number of fields, and has been considered by mainly two different perspectives: frame-like or metric-like formalisms.Important progress on HS cubic interactions in the frame-like approach was obtained by Fradkin and Vasiliev (FV) [31,32] who extended the gravitational minimal coupling to s 1 −s 2 −s 3 HS couplings. Their construction of cubic couplings is consistent in (Anti) de Sitter ((A)dS) backgrounds, and one of its essential features is the presence of inverse powers of the cosmological constant. Very recently, these interaction vertices in AdS 4 were generalized to AdS d [33] , that were conjectured to cover all vertices that can be constructed in terms of connection one-forms and curvature two-forms of symmetric HS gauge fields. In fact, the goal of the present paper is the same as that of [33], and it would be in principle interesting to explore the relation of our results with those of [33]. This comparison is although non-trivial since the two constructions use very different mathematical devices, and we will only discuss in the conclusion how the FV structure of the vertices is recovered in our approach. See [34][35][36][37] for other recent developments in the frame-like approach to the cubic-interaction problem.On the other hand, the flat-space cubic vertices of HS gauge fields in the metric-like formalism were investigated first by Berends, Burgers and van Dam [38,39], and then by many other authors. 4 Notably, the consistent vertices were classified by Metsaev [40][41][42] in terms of the number of derivatives within the lightcone approach. Despite various efforts made along the years by a number of authors, only recently has it been possible to arrive at a covariant description of all bosonic flat-space cubic interactions by Manvelyan, from a field theoretical perspective. At the...

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On nonlinear higher spin curvature

Cited by 19 publications

References 40 publications

Cubic vertices for symmetric higher-spin gauge fields in

Cubic vertices for symmetric higher-spin gauge fields in

Generalized connections and higher spin equations

Cubic interactions of massless higher spins in (A)dS: Metric-like approach

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