Higher-loop amplitudes in the non-minimal pure spinor formalism

Understand

We analyze the properties of the non-minimal pure spinor formalism.

• We show that Siegel gauge on massless vertex operators implies the primary field constraint and the level-matching condition in closed string theory by reconstructing the integrated vertex operator representation from the unintegrated ones.
• The pure spinor integration in the non-minimal formalism needs a regularisation.
• To this end we introduce a new regulator for the pure spinor integration and an extension of the regulator to allow for the saturation of the fermionic d-zero modes to all orders in perturbation.