Explaining the Pure Spinor Formalism for the Superstring
Abstract
After adding a pair of non-minimal fields and performing a similarity transformation, the BRST operator in the pure spinor formalism is expressed as a conventional-looking BRST operator involving the Virasoro constraint and (b,c) ghosts, together with 12 fermionic constraints. This BRST operator can be obtained by gauge-fixing the Green-Schwarz superstring where the 8 first-class and 8 second-class Green-Schwarz constraints are combined into 12 first-class constraints. Alternatively, the pure spinor BRST operator can be obtained from the RNS formalism by twisting the ten spin-half RNS fermions into five spin-one and five spin-zero fermions, and using the SO(10)/U(5) pure spinor variables to parameterize the different ways of twisting. GSO(-) vertex operators in the pure spinor formalism are constructed using spin fields and picture-changing operators in a manner analogous to Ramond vertex operators in the RNS formalism.
Keywords
Cite
@article{arxiv.0712.0324,
title = {Explaining the Pure Spinor Formalism for the Superstring},
author = {Nathan Berkovits},
journal= {arXiv preprint arXiv:0712.0324},
year = {2008}
}
Comments
Added two footnotes and references to Baulieu et al