Area-Preserving Diffeomorphisms and Higher-Spin Algebras

We show that there exists a one-parameter family of infinite-dimensional algebras that includes the bosonic d = 3 Fradkin-Vasiliev higher-spin algebra and the non-Euclidean version of the algebra of area-preserving diffeomorphisms of the two-sphere S2 as two distinct members. The non-Euclidean version of the area preserving algebra corresponds to the algebra of area-preserving diffeomorphisms of the hyperbolic space S1,1, and can be rewritten as lim(N→∞) su(N, N). As an application of our results, we formulate a new d = 2 + 1 massless higher-spin field theory as the gauge theory of the area-preserving diffeomorphisms of S1,1.