In Lagrangian gauge systems, the vector space of global reducibility parameters forms a module under the Lie algebra of symmetries of the action. Since the classification of global reducibility parameters is generically easier than the classification
of symmetries of the action, this fact can be used to constrain the latter when knowing the former. We apply this strategy and its generalization for the non-Lagrangian setting to the problem of conformal symmetry of various free higher spin gauge fields. This scheme allows one to show that, in terms of potentials, massless higher spin gauge fields in Minkowski space and partially-massless fields in (A)dS space are not conformal for spin strictly greater than one, while in terms of curvatures, maximal-depth partially-massless fields in four dimensions are also not conformal, unlike the closely related, but less constrained, maximal-depth Fradkin--Tseytlin fields.
Vasilievs higher-spin theories in various dimensions are uniformly represented as a simple system of equations. These equations and their gauge invariances are based on two superalgebras and have a transparent algebraic meaning. For a given higher-sp
in theory these algebras can be inferred from the vacuum higher-spin symmetries. The proposed system of equations admits a concise AKSZ formulation. We also discuss novel higher-spin systems including partially-massless and massive fields in AdS, as well as conformal and massless off-shell fields.
We elaborate on the recently proposed Lagrangian parent formulation. In particular, we identify a natural choice of the allowed field configurations ensuring the equivalence of the parent and the starting point Lagrangians. We also analyze the struct
ure of the generalized auxiliary fields employed in the parent formulation and establish the relationship between the parent Lagrangian and the recently proposed Lagrange structure for the unfolded dynamics. As an illustration of the parent formalism a systematic derivation of the frame-like Lagrangian for totally symmetric fields starting from the Fronsdal one is given. We also present a concise and manifestly sp(2)-symmetric form of the off-shell constraints and gauge symmetries for AdS higher spin fields at the nonlinear level.
The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of Lagrangian systems. It is shown that for diffeomorphism-invariant theories the parent formulation takes the form of an AKSZ-type sigm
a model. The proposed formulation can be also seen as a Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach. We also discuss its possible interpretation as a multidimensional generalization of the Hamiltonian BFV--BRST formalism. The general construction is illustrated by examples of (parametrized) mechanics, relativistic particle, Yang--Mills theory, and gravity.
Starting with an indecomposable Poincare module M_0 induced from a given irreducible Lorentz module we construct a free Poincare invariant gauge theory defined on the Minkowski space. The space of its gauge inequivalent solutions coincides with (in g
eneral, is closely related to) the starting point module M_0. We show that for a class of indecomposable Poincare modules the resulting theory is a Lagrangian gauge theory of the mixed-symmetry higher spin fields. The procedure is based on constructing the parent formulation of the theory. The Labastida formulation and the unfolded description of the mixed symmetry fields are reproduced through the appropriate reductions of the parent formulation. As an independent check we show that in the momentum representation the solutions form a unitary irreducible Poincare module determined by the respective module of the Wigner little group.
