Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-12-07
J.Math.Phys. 46 (2005) 042308
Physics
High Energy Physics
High Energy Physics - Theory
16 Pages, LaTeX2e, references added, typesetting fixed, Journal ref added
Scientific paper
10.1063/1.1863652
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.
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