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Sebastian Guttenberg, CAMGSD

Pure Spinor Superspace: on BRST Cohomology, Globality and Holomorphicity

Linearized ten dimensional super Yang Mills equations as well as supergravity can be conveniently formulated as cohomology equations of a (BRST) differential. To this end, superspace is extended with commuting spinorial coordinates that obey the so-called pure spinor constraint. The BRST differential acts on holomorphic functions deﬁned on this ”pure spinor superspace”. For the analysis of the cohomology it would be extremely useful to identify a reduced ”physical pure spinor superspace” parametrized by coordinates that are in the Kernel of the BRST differential. One way of deﬁning such BRST invariant coordinates is to solve the pure spinor constraint explicitly in local coordinate patches. An alternative way is to introduce the complex conjugate of the pure spinor. One thus either looses globality or holomorphicity and has to take care of this loss. This approach has certain similarities with the so-called harmonic superspace in four dimensions. I may or may not have the time to point them out. Note that this is an ongoing project with Antonio Grassi from Alessandria which unfortunately is still missing a conclusion. Comments different from ”that’s all trivial” and ”there is a no-go-theorem” are thus very welcome.