Abstract
It is well known in NSR string theory, that vertex operators can be constructed in various “pictures”. Recently this was discussed in the context of pure spinor formalism. NSR picture changing operators have an elegant super-geometrical interpretation. In this paper we provide a generalization of this super-geometrical construction, which is also applicable to the pure spinor formalism.
Highlights
The pure spinor target space can be considered a generalization of the odd tangent bundle ΠT X over the super-space-time X
It is well known in NSR string theory, that vertex operators can be constructed in various “pictures”
This was discussed in the context of pure spinor formalism
Summary
When studying a supermanifold X, it is often useful to consider, for any “test” supermanifold S, the space of maps: FX [S] = Map(S, X). Bernstein’s lectures in [16], which are available online at https://www.math.ias.edu/QFT/fall/). This defines a contravariant functor S → FX [S] from supermanifolds to sets. This is the “functor of points”; FX [S] is called S-points of X. If X is a supermanifold, functor ΠT in the category of supermanifolds is defined as follows: Map(S, ΠT X) = Map(S × R0|1, X). The Lie algebra of ΠT G is usually called “cone of g” and denoted Cg: Cg = LieΠT G (2.3)
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