Light-Cone Parametrizations for K\"Ahler Manifolds

TL;DR

This paper demonstrates that any K"ahler manifold can be parametrized to have a metric form similar to the light-cone metric, facilitating gauge changes in W gravities and connecting different gauges via W-geometry.

Contribution

It introduces a new parametrization of K"ahler manifolds that aligns their metrics with light-cone structures, enabling gauge transformations in W gravities.

Findings

Existence of light-cone-like parametrizations for all K"ahler manifolds

Facilitates gauge changes in W gravities

Links conformal (Toda) gauge to light-cone gauge

Abstract

It is shown that, for any K\"ahler manifold, there exist parametrizations such that the metric takes a block-form identical to the light-cone metric introduced by Polyakov for two-dimensional gravity. Besides its possible relevence for various aspects of K\"ahlerian geometry, this fact allows us to change gauge in W gravities, and explicitly go from the conformal (Toda) gauge to the light-cone gauge using the W-geometry we proposed earlier (this will be discussed in detail in a forthcoming article).