Supersymmetric structure of the induced W gravities

TL;DR

This paper explores the supersymmetric structure of W-gravities, connecting it to various theories and deriving key actions using a geometric framework with new variables.

Contribution

It introduces a new basis of variables within a geometric framework to analyze the supersymmetric structure of W-gravities and derives the Wess-Zumino-Polyakov action from Chern-Simons theory.

Findings

Identifies supersymmetric structures in W-gravities.

Derives Wess-Zumino-Polyakov action from Chern-Simons theory.

Establishes connections with Yang-Mills and topological theories.

Abstract

We derive the supersymmetric structure present in W-gravities which has been already observed in various contexts as Yang-Mills theory, topological field theories, bosonic string and chiral W_{3}-gravity. This derivation which is made in the geometrical framework of Zucchini, necessitates the introduction of an appropriate new basis of variables which replace the canonical fields and their derivatives. This construction is used, in the W_{2}-case, to deduce from the Chern-Simons action the Wess-Zumino-Polyakov action.