Pure spinor string postulates (among other things) that the classical backgrounds of the Type IIB SUGRA are in one-to-one correspondence with the classical 2d sigma-models satisfying certain additional requirements.
The -model should be classically conformally invariant
- The -model should be classically invariant under a fermionic symmetry which is nilpotent: ; it is usually called “BRST symmetry”. Moreover:
The -model should be classically invariant under two symmetries called “left and right ghost number”
The BRST operator splits into two parts: where has left ghost number +1 and right ghost number 0, and has left ghost number 0 and right ghost number +1. The and should be separately nilpotent.