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

TL;DR

This paper develops a worldline framework for bi-adjoint scalars, revealing their symmetry structure and providing new computational tools for their quantum properties, including beta functions and self-energy corrections.

Contribution

It introduces a novel worldline approach to bi-adjoint scalars, connecting vertex operators to gauge and gravity couplings, and extends to particles with complex symmetry representations.

Findings

Recovered the vanishing one-loop beta function in six dimensions.

Computed the self-energy correction to the propagator.

Extended the model to multi-adjoint particles with consistent beta functions.

Abstract

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