Cubic vertices for symmetric higher-spin gauge fields in

Abstract

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

Cubic interaction vertices for continuous-spin fields and arbitrary spin massive fields

“…In the framework of framelike approach, interacting higher-spin AdS fields are considered in refs. [47][48][49][50], while, in the framework of ambient space metric-like approach, interacting higher-spin AdS fields are considered in refs. [51][52][53][54][55][56].…”

Notes on higher-spin algebras: minimal representations and structure constants

“…For hs(so N ) and hs λ (sl 2 ) the bilinear forms have been obtained respectively in [68] and [14]. Let us remark as well that the structure constants of hs(so 5 ) and hs λ (sl 2 ) have been proposed respectively in [5] and [15][16][17].…”

“…which has been obtained in [68] in a different notation. The n = 3 case requires more involved computations -see section 3.4 -and we get in the end 62) where Λ(W ) and Σ(W ) are given by…”

“…Here, the matrices A i are in the minimal coadjoint orbit, so either U i , V i or W i depending on whether we consider sp 2N , sl N or so N . Because the minimal orbit matrices A i admit the parameterizations (2.34), they enjoy the following property: 68) where (Ā i ) jk = δ ij A jk , and A ij are given by…”

Higher-spin fermionic gauge fields and their electromagnetic coupling

“…For AdS space, in particular, those could be avoided by using the ambient-space formulation [68][69][70]. If so, one would be able to construct off-shell vertices for AdS, and compare them with the recently-obtained results of [71][72][73][74][75][76]. This would be one step towards finding a standard action for the Vasiliev systems [77][78][79][80], which are a consistent set of non-linear equations for symmetric tensors of arbitrary rank in any number of dimensions.…”