Integrated vertex operators
It is interesting to follow what happens when we deform .
In string theory, such deformations correspond to integrated vertex operators.
      
      
     ← local operator of conformal dimension 

  
In order for this new
to satisfy the Master Equation to the first order in
we require:
Such deformations correspond to deforming the target space. A natural question is:
It turns out that we also
have to deform . For every
we have to find such
that:
Moreover, the quadratic function
defined by the equation
also
deforms:
Remember that the construction of equivariant form
requires solving the equation:
And the string measure deforms:
In the base form
we substitute for
the curvature of the connection — the 2form.
Therefore:
when we turn on the vertex operator, we should also deform the 2form part of the measure
If the theory has ghost number, then
has ghost number zero and
has ghost number
.