Master Action in flat space
The case of flat space in pure spinor formalism is actually a somewhat singular limit of the general
curved background. The coefficient in front of 
goes to
infinity; one needs to pass to the first order formalism 
.
(Explicit formulas can be found here.)The main formulas are listed here.
The fundamental fields are
.
It is useful to introduce in addition the following composite fields 
,
which are defined in terms of those fundamental:
(TODO: verify coefficients):
.
It is useful to introduce in addition the following composite fields ,
which are defined in terms of those fundamental:
(TODO: verify coefficients):
The BV Master Action is:
|
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Notice that both 
and 
are constrained:
and are constrained:
The Hamiltonian generating the action of left conformal transformations on the left fields is easy to write:
It must be true that it is BV-exact:
where 
is the BV Hamiltonian generating the holomorphic symmetry corresponding to
the Noether charge 
.
Notice that 
as a consequence of the nilpotence
of the 
-ghost.
is the BV Hamiltonian generating the holomorphic symmetry corresponding to
the Noether charge .
Notice that as a consequence of the nilpotence
of the -ghost.
