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

TL;DR

This paper investigates the non-minimal pure spinor formalism in string theory, introducing a new regulator for pure spinor integration, and analyzes the four-graviton amplitude at all orders of perturbation.

Contribution

It provides a novel regularization method for pure spinor integration and explores the properties of higher-loop amplitudes in the non-minimal formalism.

Findings

Reconstructed integrated vertex operators from unintegrated ones.

Introduced a new regulator for pure spinor integration.

Analyzed four-graviton amplitude to all genus orders.

Abstract

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. We conclude with a preliminary analysis of the properties of the four-graviton amplitude to all genus order.