Integrated vertex = deformation of the action

Suppose that we infinitesimally deformed the solution of the Master Equation by adding to it some integrated vertex operator :

(1)

In order for this to satisfy the Master Equation to the first order in we require:

(2)

as we deform , what should we do with ?

The answer is simple if satisfies the Siegel gauge:

(3)

In this case remains undeformed.

On the next page we will explain what happens when Eq. (3) is not satisfied.