Pure spinors, function superspaces and supergravity theories in ten and eleven dimensions

Abstract

The constraints of d = 10 supergravity coupled to super Yang-Mills and d = 11 supergravity are studied from the viewpoint of the differential geometry of certain function superspaces. For d = 10 the appropriate function space is loop superspace, and the presence of Chern-Simons terms in the coupling of supergravity to Yang-Mills is incorporated into the formalism via a central extension of the loop group of the Yang-Mills group. For d = 11 the function superspace is the space of maps from a compact two-manifold to superspace. In both cases the superspaces include additional commuting coordinates which are pure spinors.