Spinorial cohomology and maximally supersymmetric theories

Abstract

Fields in supersymmetric gauge theories may be seen as elements in a spinorial cohomology. We elaborate on this subject, specialising to maximally supersymmetric theories, where the superspace Bianchi identities, after suitable conventional constraints are imposed, put the theories on shell. In these cases, the spinorial cohomologies describe in a unified manner gauge transformations, fields and possible deformations of the models, e.g. string-related corrections in an α ′ expansion. Explicit cohomologies are calculated for super-Yang-Mills theory in D = 10, for the N = (2, 0) tensor multiplet in D = 6 and for supergravity in D = 11, in the latter case from the point of view of both the super-vielbein and the super--form potential. The techniques may shed light on some questions concerning the α ′ -corrected effective theories, and result in better understanding of the rôle of the -form in D = 11 supergravity.

On the cohomology and inner products of the Berkovits superparticle and superstring

“…Also, a direct computation of the representation content of this cohomology was made [7] using the computer program LiE [11], which agrees with…”

Operators on Pure Spinor Spaces

“…The fact that pure spinors had a rôle to play in maximally supersymmetric models was recognised early by Nilsson [1] and Howe [2,3]. Pure spinor superfields were developed with the purpose of covariant quantisation of superstrings by Berkovits [4,5,6,7] and the cohomological structure was independently discovered in supersymmetric field theory and supergravity, originally in the context of higher-derivative deformations [8,9,10,11,12,13,14,15]. The present lecture only deals with pure spinors for maximally supersymmetric field theory.…”

“…[18], [19]. Also gravitational models have been considered [10], [13], although all that is known in such cases is that the linearised theory arises as pure spinor cohomology.…”

Origin of the pure spinor and Green-Schwarz formalisms

“…This was verified in light-cone gauge for the d=11 GS superparticle, and was verified covariantly for the d=11 pure spinor superparticle in [17,19,20]. The classical twistor-like action for the d=11 superparticle is the obvious generalization of (2.8) and is given by…”