Pure spinor partition function and the massive superstring spectrum

Abstract

We explicitly compute up to the fifth mass-level the partition function of ten-dimensional pure spinor worldsheet variables including the spin dependence. After adding the contribution from the (x(mu), theta(alpha), p(alpha)) matter variables, we reproduce the massive superstring spectrum.Even though pure spinor variables are bosonic, the pure spinor partition function contains fermionic states which first appear at the second mass-level. These fermionic states come from functions which are not globally defined in pure spinor space, and are related to the b ghost in the pure spinor formalism. This result clarifies the proper definition of the Hilbert space for pure spinor variables.