Abstract
We study the problem of interacting theories with (partially)-massless and conformal higher spin fields without matter in three dimensions. A new class of theories that have partially-massless fields is found, which significantly extends the well-known class of purely massless theories. More generally, it is proved that the complete theory has to have a form of the flatness condition for a connection of a Lie algebra, which, provided there is a non-degenerate invariant bilinear form, can be derived from the Chern-Simons action. We also point out the existence of higher spin theories without the dynamical graviton in the spectrum. As an application of a more general statement that the frame-like formulation can be systematically constructed starting from the metric one by employing a combination of the local BRST cohomology technique and the parent formulation approach, we also obtain an explicit uplift of any given metric-like vertex to its frame-like counterpart. This procedure is valid for general gauge theories while in the case of higher spin fields in d-dimensional Minkowski space one can even use as a starting point metric-like vertices in the transverse-traceless gauge. In particular, this gives the fully off-shell lift for transverse-traceless vertices.
Highlights
AND MAIN RESULTSMassless higher spin fields, as well as the graviton, do not have any propagating degrees of freedom in three dimensions
As an application of a more general statement that the framelike formulation can be systematically constructed starting from the metric one by employing a combination of the local BRST cohomology technique and the parent formulation approach, we obtain an explicit uplift of any given metriclike vertex to its framelike counterpart
As we demonstrate in this work, this allows one to explicitly construct framelike vertices starting from a representative of the respective cohomology class in the minimal model of the BRST complex and gives a systematic way to construct the framelike counterpart of a given
Summary
As well as the graviton, do not have any propagating degrees of freedom in three dimensions. It is shown that the transverse-traceless gauge condition, which is usually used in the metriclike language, can always be lifted The latter two statements are true for any spacetime dimension; (iii) we prove that all diffeomorphism invariant higher spin gravities without propagating matter and involving massless, partially-massless and conformal higher spin fields have to have the form of the flatness condition for a certain higher spin algebra; (iv) provided the algebra admits a nondegenerate invariant bilinear form, the equations can be obtained from the Chern-Simons action. IV, where we complete the Noether procedure and prove the theories in question to have the Chern-Simons form as was anticipated in [38] for massless higher spin fields
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