Proca Theory from the Spinning Worldline

TL;DR

This paper derives Proca field theory from a quantized supersymmetric worldline approach, introducing a novel BRST-based method that includes St"uckelberg fields and explores non-abelian and coupled extensions.

Contribution

It presents a new derivation of Proca theory using the quantization of an $ =2$ supersymmetric worldline with an extended BRST algebra, including St"uckelberg fields and interactions.

Findings

Derived Proca equations as BRST consistency conditions.

Proposed a cubic action reproducing the Proca action.

Explored non-abelian and dilaton couplings.

Abstract

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 St\"uckelberg 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.