Cubic Vertices for Symmetric Higher-Spin Gauge Fields in $(A)dS_d$

Details Cubic Vertices for Symmetric Higher-Spin Gauge Fields in $(A)dS_d$ Cubic Vertices for Symmetric Higher-Spin Gauge Fields in $(A)dS_d$

2011-08-30

arxiv.org/abs/1108.5921v3

Physics

High Energy Physics

High Energy Physics - Theory

78 pages. V2: typos corrected, coefficients in sections 5.1 and 6.3 corrected and undetermined coefficients of the supertrace

Scientific paper

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 $s\geq 2$, 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 $s\geq 2$ 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 $\hbar$ of the higher-spin algebra to the $(A)dS$ radius.

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