Self-dual models in D=2+1 from dimensional reduction

Abstract

Here we perform a Kaluza–Klein dimensional reduction of Vasiliev's first-order description of massless spin-s particles from D=3+1 to D=2+1 and derive first-order self-dual models describing particles with helicities ±s for the cases s=1,2,3. In the first two cases we recover known (parity singlets) self-dual models. In the spin-3 case we derive a new first order self-dual model with a local Weyl symmetry which lifts the traceless restriction on the rank-3 tensor. A gauge fixed version of this model corresponds to a known spin-3 self-dual model. We conjecture that our procedure can be generalized to arbitrary integer spins.