Vertex operators

In the rest of this talk we explain how to derive the field and Eqs. (11).

The space of SUGRA solutions should correspond to the space of sigma-models with BRST structure.

The deformation of the action can be described by vertex operators.

There are 2 types of vertex operators: integrated vertex operators and unintegrated vertex operators. It is easier to understand integrated vertex operators. They are simply the deformations of the action (1):


This is called integrated vertex. We have to require that the deformed action (12) still has the BRST structure. This is equivalent to the existence of such that:


Here means “equal on-shell”. It turns out that (13) automatically implies the existence of such that:


Notice that is an operator of engineering dimension 0 and ghost number 2. It is called unintegrated vertex.