Pure Spinor String and Generalized Geometry

TL;DR

This paper extends generalized geometry to accommodate pure spinor string theory in curved backgrounds, providing a unified Hamiltonian framework and analyzing symmetries to recover known results.

Contribution

It introduces an extended form of generalized geometry tailored for pure spinor strings and applies Hamiltonian formalism to analyze symmetries in curved backgrounds.

Findings

Extended generalized geometry for pure spinor strings

Unified Hamiltonian description of matter and ghosts

Reproduction of known symmetry conditions in new framework

Abstract

We consider the pure spinor sigma model in an arbitrary curved background. The use of Hamiltonian formalism allows for a uniform description of the worldsheet fields where matter and ghosts enter the action on the same footing. This approach naturally leads to the language of generalized geometry. In fact, to handle the pure spinor case, we need an extension of generalized geometry. In this paper, we describe such an extension. We investigate the conditions for existence of nilpotent holomorphic symmetries. In the case of the pure spinor string in curved background, we translate the existing computations into this new language and recover previously known results.