Abstract
The coupling of spin-3 gauge fields to three-dimensional Maxwell and AdS-Lorentz gravity theories is presented. After showing how the usual spin-3 extensions of the AdS and the Poincaré algebras in three dimensions can be obtained as expansions of sl(3,R) algebra, the procedure is generalized so as to define new higher-spin symmetries. Remarkably, the spin-3 extension of the Maxwell symmetry allows one to introduce a novel gravity model coupled to higher-spin topological matter with vanishing cosmological constant, which in turn corresponds to a flat limit of the AdS-Lorentz case. We extend our results to define two different families of higher-spin extensions of three-dimensional Einstein gravity.
Highlights
Higher-spin (HS) fields have received renewed interest over the last years due to their appearance in the spectrum of string theory, as well as in simplified models of the AdS/CFT correspondence [1,2,3,4]
We show that Maxwell gravity coupled to spin-3 fields can be recovered as a flat limit of the HS extension of the AdS-Lorentz case
It is well known that Poincaregravity can be recovered from the AdS case through a flat limit, which can be generalized to the case of SL (3, R) × SL (3, R) HS gravity
Summary
Higher-spin (HS) fields have received renewed interest over the last years due to their appearance in the spectrum of string theory, as well as in simplified models of the AdS/CFT correspondence [1,2,3,4] (for more recent developments see [5,6,7,8,9]). In the present paper we further generalize the coupling of spin-3 fields to gravity theories in three dimensions. After studying how the known results of HS gravity in three-dimensions fit in the framework of the expansion method, we extend the three-dimensional Maxwell [52] and AdSLorentz [49, 51] CS gravity theories to a more general setup that include spin-3 gauge fields. We show that Maxwell gravity coupled to spin-3 fields can be recovered as a flat limit of the HS extension of the AdS-Lorentz case. Present two different families of gravity theories coupled to spin-3 fields that correspond to HS extensions of the Bm and the Cm algebras and generalize the AdS and the AdS-Lorentz cases as well as their respective flat limits.
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