Superconformal theories from Pseudoparticle Mechanics

TL;DR

This paper introduces a pseudoparticle mechanical model based on Osp(N|2M) symmetry that encodes extended superconformal symmetries and provides new insights into super W-algebras and transformations.

Contribution

It presents a novel phase space gauge theory framework for superconformal symmetries, deriving super W-algebras and transformations from pseudoparticle models.

Findings

Derivation of super W-algebras from pseudoparticle models

New derivations of super Schwarzian derivatives for N=1,2

Interpretation of superconformal transformations as deformations of flags

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 ${\cal W}$-algebras. 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.