On the Relation between Hybrid and Pure Spinor String Theory

TL;DR

This paper explores the connections between different six-dimensional superstring formalisms, deriving pure spinor actions from Green-Schwarz models and relating hybrid and pure spinor approaches.

Contribution

It introduces a new hybrid pure spinor construction for six-dimensional superstrings and relates it to existing formalisms, enhancing understanding of their interrelations.

Findings

Derived six-dimensional pure spinor action from Green-Schwarz gauge-fixing.

Established a relation between hybrid pure spinor and Berkovits-Vafa-Witten formalisms.

Clarified the role of RNS variables in the hybrid formalism.

Abstract

In this paper we revisit Berkovits' pure spinor formalism in lower dimensions. We are particularly interested in relating a six-dimensional pure spinor action previously constructed in the literature to other superstring formalisms. In order to gain some insight into six-dimensional pure spinors, we first derive their action by gauge-fixing the classical six-dimensional Green-Schwarz action. We then consider a hybrid pure spinor construction in which the spacetime symmetries of six of the ten dimensions are described in pure spinor variables, while the remaining four dimensions are parameterized in terms of RNS variables. We relate this pure spinor formalism to the Berkovits-Vafa-Witten hybrid formalism of string theory on R^6 x T^4.