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
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
Moreover, the quadratic function
defined by the equation
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 2-form.
when we turn on the vertex operator, we should also deform the 2-form part of the measure
If the theory has ghost number, then
has ghost number zero and
has ghost number