On higher spin extension of the Jackiw-Teitelboim gravity model

TL;DR

This work formulates AdS$_2$ higher spin gravity as a topological BF theory with fields in $sl(N,\mathbb{R})$, embedding the Jackiw-Teitelboim sector as part of a finite higher-spin spectrum. Upon linearization around $AdS_2$, the higher-spin modes decouple into independent spin sectors $s=2,\dots,N$, yielding topological, partially-massless fields with $m_s^2 = s(s-1)\Lambda$ and no local propagating degrees of freedom. It reveals two dynamically equivalent metric-like descriptions: a standard realization where a scalar $\varphi$ satisfies $(\Box_{AdS_2}-m_s^2)\varphi=0$, and a dual realization where dynamics are encoded as conserved higher-spin currents $J_{a_1\dots a_s}$. The spin-2 case clarifies these dual pictures, and the framework lays groundwork for interacting AdS$_2$ higher-spin theories via current couplings and the unfolded approach, with potential extensions to infinite-dimensional algebras and holographic interpretations.

Abstract

We formulate AdS_2 higher spin gravity as BF theory with fields taking values in sl(N,R) 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 AdS_2 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.