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 $\pm s$ 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.