Supersymmetry on manifolds

Supersymmetry is traditionally thought of as an extension of the classical Lie-algebras describing the isometries, or conformal isometries, of Minkowski space and its cousins in different metric signatures. The corresponding algebraic structure is conveniently formalized by the concept of a super-, or graded-, Lie-algebra. The superalgebras relevant for physical applications were classified in the late 70's by Nahm, using results of Kac.

One may also consider supersymmetric extensions of the algebras of conformal isometries of more general manifolds. The corresponding algebraic structure was proposed by us to be that of a ``conformal Killing superalgebra''. I report on their definition and classification. Such algebras arise as symmetries of classical field theories such as Yang-Mills-type theories on certain manifolds. One may ask to what extent these symmetries are still realized in the corresponding quantum theories. I give precise criteria in the context of a particularly interesting field theory.

Joint work with Paul deMedeiros.