Proca Theory from the Spinning Worldline

We obtain Proca field theory from the quantisation of the $\mathcal{N}=2$ supersymmetric worldline upon supplementing the graded BRST-algebra with an extra multiplet of oscillators. The linearised theory describes the BV-extended spectrum of Proca theory, together with a Stückelberg field. When coupling the theory to background fields we derive the Proca equations, arising as consistency conditions in the BRST procedure. We also explore non-abelian modifications, complexified vector fields as well as coupling to a dilaton field. We propose a cubic action on the space of BRST-operators which reproduces the known Proca action.

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