The bundle of pure spinors
The worldsheet theory has spinor ghosts and .
Because, as we explained, they are in some sense infinitesimal objects,
we should tell them to live in some nontrivial bundle over spacetime. The transition functions of that bundle
should respect the pure spinor constraints
. This means that the
transition functions should belong to:

We will formulate the sigmamodel so that the target space is , but there is a gauge symmetry projecting .
This is how the sigmamodel for is constructed. The target space is
, but with the gauge symmetry .