Worldline description of a bi-adjoint scalar and the zeroth copy

Bi-adjoint scalars are helpful in studying properties of color/kinematics duality and the double copy, which relates scattering amplitudes gauge gravity theories. Here we study bi-adjoint from a worldline perspective. We show how global $G \times \tilde G$ symmetry group may be realized by degrees freedom. The action gives rise to vertex operators, compared similar ones describing coupling fields gravity, thus exposing interplay this framework. is quantized path integrals find representation one-loop QFT effective scalar cubic theory. As simple applications, recover beta function theory six dimensions, verifying its vanishing, compute self-energy correction propagator. model easily extendable that particle carrying an arbitrary direct products groups, including multi-adjoint particle, whose reproduce as well.