Abstract We propose a new class of conformal higher spin gravities in three dimensions, which extends the one by Pope and Townsend.The Inline - Roller Skates 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 Lunging System pointed out.