Structure of the action
The action consists of the matter term (a generic sigma-model) and some ghost terms.
The ghost terms are of the form:
|
with the following notations:
and 
are scalars on the worldsheet taking values in the spin bundle
over the target space; they satisfy the pure spinor constraints
and 
are 1-forms on the worldsheet taking values in the dual to the spin
bundle over the target space; there is some gauge symmetry because 
and 
satisfy the pure spinor constraints
is the pairing between the conjugate to the spin bundle and the spin bundlethe Dolbeault operators
and 
are
explained here
Strictly speaking, instead of and one has to use the target space-covariant
derivatives:
and one has to use the target space-covariant
derivatives:
|
where 
is some connection in the target space spin bundle.
is some connection in the target space spin bundle.There is also some quartic term 
.