Abstract
Two-dimensional BF theory with infinitely many higher spin fields is proposed. It is interpreted as the AdS(2) higher spin gravity model describing a consistent interaction between local fields in AdS(2) space including gravitational field, higher spin partially-massless fields, and dilaton fields. We carry out analysis of the frame-like and the metric-like formulation of the theory. Infinite-dimensional higher spin global algebras and their finite-dimensional truncations are realized in terms of o(2,1) - sp(2) Howe dual auxiliary variables.
Highlights
In the recent years, higher spin gauge theories in three, four and higher dimensions have attracted considerable interest, while comparatively little attention has been paid to two-dimensional higher spin theories [6,7,8,9,10,11]
We show that the σ+ cohomological reduction yields the massive scalar Klein-Gordon equation on the hyperboloid with non-vanishing right-hand-side given by scalar Weyl tensor
We proposed a new class of two-dimensional higher spin models interpreted as the AdS2 higher spin gravity and explored some of its global and local properties
Summary
Higher spin gauge theories in three, four and higher dimensions have attracted considerable interest (e.g., see reviews [1,2,3,4,5] and references therein), while comparatively little attention has been paid to two-dimensional higher spin theories [6,7,8,9,10,11]. Recall that the system does not have local degrees of freedom It follows that the AdS2 higher spin gravity can be interpreted as a consistent theory of topological yet interacting partially-massless higher spin fields given in a closed form. In this paper we formulate AdS2 higher spin gravity with (in)finitely many fields as BF theory for the infinite-dimensional higher spin gauge algebra A = hs[ν] and its finitedimensional truncations [36, 37]. The Howe duality o(2, 1) − sp(2) used to describe quotient higher spin algebras may be useful in many respects, in particular, for considering general non-linear two-dimensional higher spin models not necessarily of BF type. Details of the projecting technique are given in appendix B
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