Cubic interactions of massless bosonic fields in three dimensions

TL;DR

This paper classifies all parity-even cubic interactions of massless bosonic fields in three-dimensional Minkowski space, revealing unique vertices and derivative structures depending on spins and couplings.

Contribution

It provides a comprehensive classification of cubic vertices for massless bosons in 3D, highlighting differences from higher dimensions and analyzing minimal couplings.

Findings

At most one vertex per spin triple in 3D.

Vertices with more than three derivatives involve scalar and Maxwell fields.

Universal minimal gravity coupling applies to all spins.

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.