Pure spinors in AdS and Lie algebra cohomology

TL;DR

This paper explores the algebraic structure of the BRST cohomology in Type IIB superstring theory on AdS5xS5, revealing new insights into vertex operators and their algebraic descriptions.

Contribution

It introduces a novel algebraic framework using Lie superalgebra cohomology to describe BRST states and vertex operators in superstring theory.

Findings

Vertex operators of ghost number 1 are characterized as conserved currents.

New algebraic description of ghost number 2 vertices is provided.

Clarification of zero mode sector structure in flat space and initial study of higher ghost number vertices.

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.