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Origin of the pure spinor and Green-Schwarz formalisms

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Author(s):
Berkovits, Nathan
Total Authors: 1
Document type: Journal article
Source: Journal of High Energy Physics; v. N/A, n. 7, p. 20-pg., 2015-07-20.
Abstract

The pure spinor formalism for the superstring was recently obtained by gauge-fixing a purely bosonic classical action involving a twistor-like constraint a,x (m) (gamma (m) lambda) (alpha) = 0 where lambda (alpha) is a d=10 pure spinor. This twistor-like constraint replaces the usual Virasoro constraint a,x (m) a,x (m) = 0, and the Green-Schwarz fermionic spacetime spinor variables theta (alpha) 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 lambda (alpha) 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 , this action can be interpreted as a standard A parts per thousand = 5 topological action where one integrates over the 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. (AU)

FAPESP's process: 11/11973-4 - ICTP South American Institute for Fundamental Research: a regional center for theoretical physics
Grantee:Nathan Jacob Berkovits
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 09/50639-2 - Research and learning on the strings theory
Grantee:Nathan Jacob Berkovits
Support Opportunities: Research Projects - Thematic Grants