On Extensions of Superconformal Algebras
arXiv:hep-th/0412061 · doi:10.1063/1.1863652
Abstract
Starting from vector fields that preserve a differential form on a Riemann sphere with Grassmann variables, one can construct a Superconformal Algebra by considering central extensions of the algebra of vector fields. In this note, the N=4 case is analyzed closely, where the presence of weight zero operators in the field theory forces the introduction of non-central extensions. How this modifies the existing Field Theory, Representation Theory and Gelfand-Fuchs constructions is discussed. It is also discussed how graded Riemann sphere geometry can be used to give a geometrical description of the central charge in the N=1 theory.
16 Pages, LaTeX2e, references added, typesetting fixed, Journal ref added