Cubic interactions of massless bosonic fields in three dimensions

Abstract

Parity-even cubic vertices of massless bosons of arbitrary spins in three dimensional Minkowski space are classified in the metric-like formulation. As opposed to higher dimensions, there is at most one vertex for any given triple $s_1,s_2,s_3$ in three dimensions. All the vertices with more than three derivatives are of the type $(s,0,0)$, $(s,1,1)$ and $(s,1,0)$ involving scalar and/or Maxwell fields. All other vertices contain two (three) derivatives, when the sum of the spins is even (odd). Minimal coupling to gravity, $(s,s,2)$, has two derivatives and is universal for all spins (equivalence principle holds). Minimal coupling to Maxwell field, $(s,s,1)$, distinguishes spins $s\leq 1$ and $s\geq 2$ as it involves one derivative in the former case and three derivatives in the latter case. Some consequences of this classification are discussed.