Actions, Charges and Off-Shell Fields in the Unfolded Dynamics Approach

Abstract

Within unfolded dynamics approach, we represent actions and conserved charges as elements of cohomology of the L ∞ algebra underlying the unfolded formulation of a given dynamical system. The unfolded off-shell constraints for symmetric fields of all spins in Minkowski space are shown to have the form of zero curvature and covariant constancy conditions for 1-forms and 0-forms taking values in an appropriate star product algebra. Unfolded formulation of Yang-Mills and Einstein equations is presented in a closed form.

The generalized curvature and Christoffel symbols for a higher spin potential in AdSd+1 space

“…First of all this hierarchy is a full geometrical partner of Fronsdal's linearized dynamics [3] for HS gauge fields in the case of flat space and puts this theory on the same level as linearized gravity. From another hand this hierarchy should be intimately connected with the generalized Weyl tensors introduced in [4] and with the recent investigations of the so-called unfolded formulation for higher spin theories (see [5] and refs. there) which is pretending today to describe the nonlinear interaction for HS fields in a general background.…”

Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions

“…[30] for an extended discussion of this point). As far as the non-Abelian frame-like formulation is concerned, the analogue of Vasiliev's unfolded equations in the unconstrained case are also of interest for studying the off-shell gauge symmetry structure [39,40]. Moreover, a slight refinement of the on-shell unfolded equations has been proposed in [44] following the spirit of the unconstrained approach.…”

A minimal BV action for Vasiliev’s four-dimensional higher spin gravity

“…The properties of Vasiliev's theory that underlie the construction of the actions hold true in general models with Lorentzian signature and negative cosmological constant, including models with Yang-Mills sectors and supersymmetries. The offshell formulation of [1] combine the principle of unfolding [6,2,7,8,9], which lies at the heart of Vasiliev's equations, with a natural extension of the generalized Poisson sigma model from graded-commutative to graded-associative differential algebras 1 .…”