Partition Functions of Pure Spinors

TL;DR

This paper computes partition functions for pure-spinor superstrings across various dimensions, revealing the structure of massless and massive multiplets and confirming the criticality of these string theories.

Contribution

It provides explicit partition functions for pure-spinor superstrings in multiple dimensions and confirms their criticality through BRST cohomology analysis.

Findings

Massless states form a spin-one gauge multiplet.

First massive states form a massive spin-two multiplet.

Pure spinor systems are shown to be critical string theories.

Abstract

We compute partition functions describing multiplicities and charges of massless and first massive string states of pure-spinor superstrings in 3,4,6,10 dimensions. At the massless level we find a spin-one gauge multiplet of minimal supersymmetry in d dimensions. At the first massive string level we find a massive spin-two multiplet. The result is confirmed by a direct analysis of the BRST cohomology at ghost number one. The central charges of the pure spinor systems are derived in a manifestly SO(d) covariant way confirming that the resulting string theories are critical. A critical string model with N=(2,0) supersymmetry in d=2 is also described.