Pseudoduality in Supersymmetric Sigma Models

TL;DR

This paper explores the extension of pseudoduality transformations to supersymmetric sigma models, revealing conditions for invertibility, curvature, and torsion, and identifying specific cases like super WZW models with distinct pseudoduality conditions.

Contribution

It generalizes classical pseudoduality to supersymmetric models using component and coframe methods, and uncovers unique properties and conditions such as non-invertibility and curvature constraints.

Findings

Pseudoduality is not invertible at all points.

Torsion must vanish on the original manifold but not on the pseudodual.

Curvatures of the manifolds must be constant and equal.

Abstract

We study the pseudoduality transformation in supersymmetric sigma models. We generalize the classical construction of pseudoduality transformation to supersymmetric case. We perform this both by component expansion method on manifold M and by orthonormal coframe method on manifold SO(M). The component expansion method yields the result that pseudoduality tranformation is not invertible at all points and occurs from all points on one manifold to only one point where riemann normal coordinates are valid on the second manifold. Torsion of the sigma model on M must vanish while it is nonvanishing on pseudodual manifold, and curvatures of the manifolds must be constant and the same. In case of super WZW sigma models pseudoduality equations result in three different pseudoduality conditions; flat space, chiral and antichiral pseudoduality.