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

By Mikhail A. Vasiliev. 2011

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Cubic vertices for symmetric higher-spin gauge fields of integer spins in (A)dSd are analyzed. (A)dSd generalization of the previously known action in AdS4, 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)dSd, 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 AdSd 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 ℏ of the higher-spin algebra to the (A)dS radius.

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Citations in the corpus

Elements of Vasiliev theory (2014, methodology): “A lot is known about cubic interactions both in the metric-like approach of Fronsdal [6–23] and in the frame-like approach of Vasiliev and Fradkin-Vasiliev [2–4, 24–30].”
On the uniqueness of higher-spin symmetries in AdS and CFT (2013, methodology): “This follows directly from the Fradkin-Vasiliev construction [32–34], where the deformations of the linearized field-strengths are of the Yang-Mills type and are constructed by adding all possible terms bilinear in the HS gauge connections (1.”
Towards metric-like higher spin gauge theories in three dimensions (2012, background): “5) by adding higher-derivative contributions to the action (see also [40, 11]).”
Quartic AdS interactions in higher-spin gravity from Conformal Field Theory (2015, background): “[2–26], which in particular gives a complete classification of local cubic interactions in any dimensions [10].”