A construction of integrated vertex operator in the pure spinor sigma-model in AdS5xS5

TL;DR

This paper presents a straightforward method to construct integrated vertex operators from unintegrated ones in the pure spinor formalism of string theory in AdS5xS5, using Lie superalgebra cohomology and Lax currents.

Contribution

It introduces a new, simplified approach to derive integrated vertex operators from unintegrated vertices via cocycle evaluation on Lax currents.

Findings

Simplified construction of integrated vertices from unintegrated ones.

Application of Lie superalgebra cohomology to vertex operator construction.

Clear relation established between vertex operators and Lax currents.

Abstract

Vertex operators in string theory come in two varieties: integrated and unintegrated. Understanding both types is important for the calculation of the string theory amplitudes. The relation between them is a descent procedure typically involving the b-ghost. In the pure spinor formalism vertex operators can be identified as cohomology classes of an infinite-dimensional Lie superalgebra formed by covariant derivatives. We show that in this language the construction of the integrated vertex from an unintegrated vertex is very straightforward, and amounts to the evaluation of the cocycle on the generalized Lax currents.