Interactions of a Continuous-Spin Field with a Spin-1/2 Particle

TL;DR

This paper develops a formalism for coupling continuous-spin fields with spin-1/2 particles using supersymmetric worldline methods, enabling potential phenomenological tests of deviations from standard QED.

Contribution

It introduces a new formalism for consistent interactions between continuous-spin fields and fermions, extending the theoretical framework for CSP phenomenology.

Findings

Constructed local currents respecting supersymmetry and conservation laws.

Demonstrated reduction to QED and Yukawa interactions in specific limits.

Provided a basis for studying phenomenological deviations from QED with CSPs.

Abstract

We introduce a formalism for coupling a bosonic Continuous-Spin field to familiar spin-1/2 matter. To do this, we describe the matter using the supersymmetric worldline formalism. We construct currents that are local functions of worldline kinematics, and respect both the worldline supersymmetry and the conservation condition required for consistent couplings to Abelian CSP fields. As the spin Casimir $\rho$ of the CSP vanishes, the interactions reduce to that of familiar QED in one case, and to a Yukawa interaction with a spin-1/2 fermion in another case. Our formalism is applicable to computing deviations from QED if the photon is a CSP, thereby enabling a range of phenomenological studies.