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.

arXiv comment15 pages, no figures, one added ref., added paragraph at the end of section 2, accepted in Annals Of Physics

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Cited by in corpus (1)

• Reaching out a "geometrical" description for spin-4 self-dual models in $D=2+1$