A New First Class Algebra, Homological Perturbation and Extension of Pure Spinor Formalism for Superstring

Abstract

Based on a novel first class algebra, we develop an extension of the pure spinor (PS) formalism of Berkovits, in which the PS constraints are removed. By using the homological perturbation theory in an essential way, the BRST-like charge $Q$ of the conventional PS formalism is promoted to a bona fide nilpotent charge $\hat{Q}$, the cohomology of which is equivalent to the constrained cohomology of $Q$. This construction requires only a minimum number (five) of additional fermionic ghost-antighost pairs and the vertex operators for the massless modes of open string are obtained in a systematic way. Furthermore, we present a simple composite "$b$-ghost" field $B(z)$ which realizes the important relation $T(z)=\{\hat{Q},B(z)\}$, with $T(z)$ the Virasoro operator, and apply it to facilitate the construction of the integrated vertex. The present formalism utilizes U(5) parametrization and the manifest Lorentz covariance is yet to be achieved.

arXiv comment38 pages, no figure. Proof of triviality of delta-homology improved and a reference added

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Cited by in corpus (39)

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• Relating the Green-Schwarz and Pure Spinor Formalisms for the Superstring
• Origin of Pure Spinor Superstring
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• Simplifying and Extending the AdS_5xS^5 Pure Spinor Formalism
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