The Character of Pure Spinors

TL;DR

This paper computes the character of pure spinor spaces in multiple dimensions, deriving covariant formulas for central charges and cohomology relevant to superstring and superparticle theories.

Contribution

It introduces a covariant method to derive central charges and cohomology in the pure spinor formalism, advancing understanding of superstring theory.

Findings

Calculated the character of pure spinor spaces in 10, 11, and 12 dimensions.

Derived covariant formulas for central charges in the pure spinor formalism.

Simplified the derivation of zero momentum cohomology for D=10 and D=11 superparticles.

Abstract

The character of holomorphic functions on the space of pure spinors in ten, eleven and twelve dimensions is calculated. From this character formula, we derive in a manifestly covariant way various central charges which appear in the pure spinor formalism for the superstring. We also derive in a simple way the zero momentum cohomology of the pure spinor BRST operator for the D=10 and D=11 superparticle.