Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-10-26
J.Math.Phys. 41 (2000) 7129-7161
Physics
High Energy Physics
High Energy Physics - Theory
1+46 pages, No figure, LaTeX, References added
Scientific paper
10.1063/1.1290056
Three-dimensional N-extended superconformal symmetry is studied within the superspace formalism. A superconformal Killing equation is derived and its solutions are classified in terms of supertranslations, dilations, Lorentz transformations, R-symmetry transformations and special superconformal transformations. Superconformal group is then identified with a supermatrix group, OSp(N|2,R), as expected from the analysis on simple Lie superalgebras. In general, due to the invariance under supertranslations and special superconformal transformations, superconformally invariant n-point functions reduce to one unspecified (n-2)-point function which must transform homogeneously under the remaining rigid transformations, i.e. dilations, Lorentz transformations and R-symmetry transformations. After constructing building blocks for superconformal correlators, we are able to identify all the superconformal invariants and obtain the general form of n-point functions. Superconformally covariant differential operators are also discussed.
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