Abstract
We propose a new class of conformal higher spin gravities in three dimensions, which extends the one by Pope and Townsend. The main new feature is that there are infinitely many examples of the new theories with a finite number of higher spin fields, much as in the massless case. The action has the Chern-Simons form for a higher spin extension of the conformal algebra. In general, the new theories contain Fradkin-Tseytlin fields with higher derivatives in the gauge transformations, which is reminiscent of partially-massless fields. A relation of the old and new theories to the parity anomaly is pointed out.
Highlights
These fields can be understood as boundary values of the genuine partially-massless fields in AdS4 [16]
What is interesting as compared to the case studied by Pope and Townsend is that there is a family of finite-dimensional higher spin algebras, which is similar to the purely massless case in 3d
3 New conformal higher spin theories. As it was already stated in the introduction, the main idea is to use the large stock of higher spin algebras for-massless fields, which is available in AdS4 and to add some new algebras
Summary
We briefly discuss the conformal gravity in 3d: how the simple Chern-Simons formulation is related to the one where the dynamical field is conformal graviton gμν [9]. The very first formulation of conformal gravity in three dimensions was found in the form of a nonstandard Chern-Simons action [58, 59]:. The conformal invariance of the action is not manifest This formulation is equivalent to the Chern-Simons theory of the conformal algebra so(3, 2) [9]. FKa = 0 imposes Cμν = 0, where C is the Cotton tensor The latter is the only dynamical equation. If we impose b = 0 and solve for all the auxiliary fields, i.e. f a, a,b, and plug the solution back into the Chern-Simons action (2.5) we obtain (2.1), where ea is the only dynamical variable. The action can be rewritten in terms of conformal metric gμν
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