On the $\mathcal{N}$ = 4, d = 4 pure spinor measure factor

In this work, we obtain a simple measure factor for the $\lambda$ and $\theta$ zero-mode integrations in the pure-spinor formalism in the context of an $\mathcal{N}$ = 4, d = 4 theory. We show that the measure can be defined unambiguously up to BRST-trivial terms and an overall factor, and is much simpler than (although equivalent to) the expression obtained by dimensional reduction from the $\mathcal{N}$ = 1, d = 10 measure factor. We also give two explicit examples of how to obtain the dual to a vertex operator using this measure.