Pure Spinor Partition Function and the Massive Superstring Spectrum

Understand

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.