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A CSP Field Theory with Helicity Correspondence

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 $ρ$ vanishes, the helicity correspondence is manifest -- familiar gauge theory actions are recovered and couplings to conserved currents can easily be introduced. For non-zero $ρ$, 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 $ρ$ 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.