The Geometric Structure of $W_N$-Gravity

TL;DR

This paper explores the geometric structure of W_N-gravity, deriving its non-linear action and transformations from a broader W_infinity gravity framework, and reveals a linearization via a twistor-like transform.

Contribution

It introduces a non-linear truncation method for W_N-gravity from W_infinity gravity and discusses its geometric properties and linearization techniques.

Findings

Derived the full non-linear action and transformation rules for W_N-gravity.

Showed that the defining equations become linear after a twistor-like transform.

Connected the geometry of W_N-gravity to broader W_infinity gravity structures.

Abstract

The full non-linear structure of the action and transformation rules for $\W_N$-gravity coupled to matter are obtained from a non-linear truncation of those for $w_ \infty$ gravity. The geometry of the construction is discussed, and it is shown that the defining equations become linear after a twistor-like transform.