Cubic vertices for symmetric higher-spin gauge fields in (A)dSd

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 (h) over bar of the higher-spin algebra to the (A)dS radius. (C) 2012 Elsevier B.V. All rights reserved.