Operator Space of Pure Spinors

Over the last decade, a new first quantization scheme for superstring called “pure spinor formalism” has been developed following the pioneering work of Berkovits.1) Compared to the conventional Ramond-Neveu-Schwarz (RNS) and Green-Schwarz (GS) formalisms, the new formalism has an advantage of being super-Poincare covariant at the quantum level. It has been successfully used to covariantly compute multi-loop higher-point scattering amplitudes in a flat background, and to construct string models in presence of Ramond-Ramond (RR) fluxes such as the RR supported AdS5 × S5 background. By now, it appears fair to claim that the formalism has proved its utility as a consistent first quantization scheme. Given that the pure spinor formalism gives a correct first quantized description of superstring, it is natural to seek for its application to second quantization, or superstring field theory (SSFT). The purpose of this talk was to describe the current state of the art in this direction. Let us begin with a short comparison of the pure spinor formalism with conventional formalisms. The following table summarises some features of commonly used formalisms.∗) RNS superstring is defined on a superworldsheet and powerful methods of super-