Pure spinors in AdS and Lie algebra cohomology

Abstract

We show that the BRST cohomology of the massless sector of the Type IIB superstring on AdS5xS5 can be described as the relative cohomology of an infinite-dimensional Lie superalgebra. We explain how the vertex operators of ghost number 1, which correspond to conserved currents, are described in this language. We also give some algebraic description of the ghost number 2 vertices, which appears to be new. We use this algebraic description to clarify the structure of the zero mode sector of the ghost number two states in flat space, and initiate the study of the vertices of the higher ghost number.Comment: 39pp. LaTeX; v2: corrections in Section 4; v3: expanded Section 4.10, added reference; v4: added example of a vertex at the ghost number 3 in Section 5.3, removed Section 4.9, added explanations; v5: corrections in Sections 3.3 and 4.