Cubic interactions of massless bosonic fields in three dimensions II: Parity-odd and Chern-Simons vertices

Understand

This work completes the classification of the cubic vertices for arbitrary spin massless bosons in three dimensions started in a previous companion paper by constructing parity-odd vertices.

• Similarly to the parity-even case, there is a unique parity-odd vertex for any given triple $s_1\geq s_2\geq s_3\geq 2$ of massless bosons if the triangle inequalities are satisfied ($s_1<s_2+s_3$) and none otherwise.
• These vertices involve two (three) derivatives for odd (even) values of the sum $s_1+s_2+s_3$.
• A non-trivial relation between parity-even and parity-odd vertices is found.