Pure Spinor Integration from the Collating Formula

TL;DR

This paper develops a mathematically rigorous BRST-invariant path integral formulation for pure spinor amplitudes by employing algebraic geometry and boundary term techniques to define a consistent integration measure.

Contribution

It introduces a novel method to construct the pure spinor integration measure using the collating formula and differential forms across algebraic geometric patches.

Findings

Defined a BRST-invariant path integral for pure spinors.

Constructed the integration measure using differential forms on algebraic patches.

Ensured a well-defined measure by adding boundary terms at intersections.

Abstract

We use the technique developed by Becchi and Imbimbo to construct a well-defined BRST-invariant path integral formulation of pure spinor amplitudes. The space of pure spinors can be viewed from the algebraic geometry point of view as a collection of open sets where the constraints can be solved and a free independent set of variables can be defined. On the intersections of those open sets, the functional measure jumps and one has to add boundary terms to construct a well-defined path integral. The result is the definition of the pure spinor integration measure constructed in term of differential forms on each single patch.