Pure spinor superstring

There are different approaches to string theory, which all start from slightly different (although similar) postulates.

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 requirements are:

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.