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 fields

Construct 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.