PureSpinorBundle

The bundle of pure spinors

and

. Because, as we explained, they are in some sense infinitesimal objects, we should tell them to live in some nontrivial bundle over space-time. The transition functions of that bundle should respect the pure spinor constraints

. This means that the transition functions should belong to:

It is useful to consider the corresponding principal bundle, which we will call .
It is constructed in the following way.
The description of the SUGRA data starts with specifying a distribution . Invariantly, this is defined as at the singular locus .
Moreover, we must have specified, for every point , an -orbit of a 32-ple in . This orbit is the fiber of over

We will formulate the sigma-model so that the target space is , but there is a gauge symmetry projecting .

This is how the sigma-model for

is constructed. The target space is

, but with the gauge symmetry

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