Left BV formalism
1 Problem
Let us consider the left deformation of the pure spinor action, analogous to Eq. (1):
The problem is:
Construct the
-exact BV Hamiltonian 
generating the action of
left-deforming vector fieldsConstruct the closed form
base with respect to this action
2 The case of conformal vector fields
Suppose that our left-deforming vector field 
is actually conformal.
In this case it is a symmetry of 
. We can describe 
as the BV
Hamiltonian corresponding to the holomorphic symmetry of , generated by the
Noether charge 
. It satisfies 
as a consequence
of the nilpotence of the 
-ghost.
3 The case of left vector fields
Let us now suppose that is a left vector field 
.
TODO, maybe this will be as easy as conformal.
4 The case of left-deforming vector fields
Now suppose that is a left-deforming vector field
.
TODO, this could be harder.