On higher spin extension of the Jackiw–Teitelboim gravity model

Abstract

We formulate two-dimensional anti-de Sitter (AdS2) higher spin gravity as BF theory with fields taking values in algebra treated as higher spin algebra. The theory is topological and naturally extends the Jackiw–Teitelboim gravity model so as to include higher spin fields. The BF equations linearized about the background are interpreted as describing higher spin partially massless fields of maximal depth along with dilaton fields. It is shown that there are dual metric-like formulations following from the original linearized BF higher spin theory. The duality establishes a dynamical equivalence of the metric-like field equations that can be given either as massive scalar field equations or as conservation conditions for higher spin currents.