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Apfeldorf K.M., Gomis J.
Superconformal theories from Pseudoparticle Mechanics
ABSTRACT. We consider a one-dimensional Osp($N|2M$) pseudoparticle
mechanical model which may be written as a phase space gauge theory.
We show how the pseudoparticle model naturally encodes and explains the
two-dimensional zero curvature approach to finding extended conformal
symmetries. We describe a procedure of partial gauge fixing of these
theories which leads generally to theories with superconformally extended
The pseudoparticle model allows one to derive the finite
transformations of the gauge and matter fields occurring in these
theories with extended conformal symmetries.
In particular, the partial gauge fixing of the Osp($N|2$) pseudoparticle
mechanical models results in theories with the
SO($N$) invariant $N$-extended superconformal symmetry algebra of
Bershadsky and Knizhnik. These algebras are nonlinear for $N \geq 3.$
We discuss in detail the cases of $N=1$ and $N=2,$ giving
two new derivations of the superschwarzian derivatives.
Some comments are made in the
$N=2$ case on how twisted and topological theories represent a
significant deformation of the original particle model.
The particle model also allows one to interpret superconformal
transformations as deformations of flags in super jet bundles over
the associated super Riemann surface.