Relating Green-Schwarz and Extended Pure Spinor Formalisms by Similarity Transformation

TL;DR

This paper constructs an explicit similarity transformation linking the light-cone Green-Schwarz and extended pure spinor formalisms of superstring theory, enhancing understanding of pure-spinor approaches.

Contribution

It introduces a systematic method to relate different superstring formalisms via similarity transformations, including the novel mapping between Green-Schwarz and extended pure spinor formalisms.

Findings

Explicit similarity transformation constructed

Operator mapping between formalisms achieved

Insights into pure-spinor formalism gained

Abstract

In order to gain deeper understanding of pure-spinor-based formalisms of superstring, an explicit similarity transformation is constructed which provides operator mapping between the light-cone Green-Schwarz (LCGS) formalism and the extended pure spinor (EPS) formalism, a recently proposed generalization of the Berkovits' formalism in an enlarged space. By applying a systematic procedure developed in our previous work, we first construct an analogous mapping in the bosonic string relating the BRST and the light-cone formulations. This provides sufficient insights and allows us to construct the desired mapping in the more intricate case of superstring as well. The success of the construction owes much to the enlarged field space where pure spinor constraints are removed and to the existence of the ``B-ghost'' in the EPS formalism.