Origin of the pure spinor and Green-Schwarz formalisms
The pure spinor formalism for the superstring was recently obtained by gauge-fixing a purely bosonic classical action involving a twistor-like constraint ∂x<sup>m</sup>(γ<inf>m</inf>λ)<inf>α</inf> = 0 where λ<sup>α</sup> is a d=10 pure spinor. This twi...
| Autor: | |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2015 |
| País: | Brasil |
| Institución: | Universidade Estadual Paulista (UNESP) |
| Repositorio: | Repositório Institucional da UNESP |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unesp.br:11449/171963 |
| Acceso en línea: | http://dx.doi.org/10.1007/JHEP07(2015)091 http://hdl.handle.net/11449/171963 |
| Access Level: | acceso abierto |
| Palabra clave: | BRST Symmetry Superstrings and Heterotic Strings |
| Sumario: | The pure spinor formalism for the superstring was recently obtained by gauge-fixing a purely bosonic classical action involving a twistor-like constraint ∂x<sup>m</sup>(γ<inf>m</inf>λ)<inf>α</inf> = 0 where λ<sup>α</sup> is a d=10 pure spinor. This twistor-like constraint replaces the usual Virasoro constraint ∂x<sup>m</sup>∂x<inf>m</inf> = 0, and the Green-Schwarz fermionic spacetime spinor variables θ<sup>α</sup> arise as Faddeev-Popov ghosts for this constraint. In this paper, the purely bosonic classical action is simplified by replacing the classical d=10 pure spinor λ<sup>α</sup> with a d=10 projective pure spinor. The pure spinor and Green-Schwarz formalisms for the superparticle and superstring are then obtained as different gauge-fixings of this purely bosonic classical action, and the Green-Schwarz kappa symmetry is directly related to the pure spinor BRST symmetry. Since a d=10 projective pure spinor parameterizes (Formula presented.), this action can be interpreted as a standard ĉ = 5 topological action where one integrates over the (Formula presented.) choice of complex structure. Finally, a purely bosonic action for the d=11 supermembrane is proposed which reduces upon double-dimensional reduction to the purely bosonic action for the d=10 Type IIA superstring. |
|---|