Yang-Mills theory and the $\mathcal{N}=2$ spinning path integral

We embed the perturbative Fock state of the Yang-Mills BV-multiplet in the vertex operator algebra of the path-integral for the \mathcal{N}=2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mstyle mathvariant="script"> <mml:mi>𝒩</mml:mi> </mml:mstyle> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> supersymmetric world line and evaluate the pull-back of the latter to an integral form on supermoduli space. Choosing a suitable Poincaré dual on the latter, we show that this integral form describes an extension of Yang-Mills theory. Upon projection back to the Fock space, we recover the Yang-Mills action from the world line. This furthermore gives an a priori justification for the construction of Yang-Mills equations of motion as emerging from deformations of the BRST differential.