Pure Spinor String and Generalized Geometry

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.