A CSP Field Theory with Helicity Correspondence

TL;DR

This paper introduces a covariant local action for a single free continuous-spin particle, revealing how helicity correspondence manifests and highlighting the structure of gauge invariance and current conservation for different spin invariants.

Contribution

It presents the first covariant local action for continuous-spin particles, formulated in a vector superspace, and explores the gauge symmetry and current structure for varying spin invariants.

Findings

Helicity correspondence is explicit when the spin invariant $ ho$ is zero.

A tower of tensor currents is necessary for non-zero $ ho$, with only the lowest being conserved.

Local gauge-invariant operators are scarce for non-zero $ ho$, implying covariant equations of motion in interactions.

Abstract

We propose the first covariant local action describing the propagation of a single free continuous-spin degree of freedom. The theory is simply formulated as a gauge theory in a "vector superspace", but can also be formulated in terms of a tower of symmetric tensor gauge fields. When the spin invariant $\rho$ vanishes, the helicity correspondence is manifest -- familiar gauge theory actions are recovered and couplings to conserved currents can easily be introduced. For non-zero $\rho$, a tower of tensor currents must be present, of which only the lowest rank is exactly conserved. A paucity of local gauge-invariant operators for non-zero $\rho$ suggests that the equations of motion in any interacting theory should be covariant, not invariant, under a generalization of the free theory's gauge symmetry.