On the BRST Cohomology of Superstrings with/without Pure Spinors

Details On the BRST Cohomology of Superstrings with/without Pure Spinors On the BRST Cohomology of Superstrings with/without Pure Spinors

2002-06-24

arxiv.org/abs/hep-th/0206216v1

Adv.Theor.Math.Phys. 7 (2003) 499-524

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, TeX

Scientific paper

We replace our earlier condition that physical states of the superstring have non-negative grading by the requirement that they are analytic in a new real commuting constant t which we associate with the central charge of the underlying Kac-Moody superalgebra. The analogy with the twisted N=2 SYM theory suggests that our covariant superstring is a twisted version of another formulation with an equivariant cohomology. We prove that our vertex operators correspond in one-to-one fashion to the vertex operators in Berkovits' approach based on pure spinors. Also the zero-momentum cohomology is equal in both cases. Finally, we apply the methods of equivariant cohomology to the superstring, and obtain the same BRST charge as obtained earlier by relaxing the pure spinor constraints.

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