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

TL;DR

This paper derives a simplified, unambiguous measure factor for pure spinor formalism in 4D N=4 theories, facilitating calculations by reducing complexity compared to higher-dimensional reductions.

Contribution

It introduces a new, simpler measure factor for pure spinor formalism in 4D N=4, ensuring unambiguous zero-mode integrations and providing explicit examples for vertex operator duals.

Findings

Measure factor is simpler and equivalent to dimensional reduction results.

Unambiguous definition up to BRST-trivial terms and overall factor.

Explicit examples demonstrate practical application in vertex operator duals.

Abstract

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.