Lectures on W algebras and W gravity

TL;DR

This paper reviews extended conformal algebras called W algebras, their structures, and their applications to W-gravity and W-string theories, highlighting their mathematical properties and physical relevance.

Contribution

It provides a comprehensive overview of various W algebras, including their classifications, structures, and roles in constructing W-gravity and W-string models.

Findings

Classification of W algebras including nonlinear and linear types

Discussion of super-extensions of W algebras

Applications to W-gravity and W-string theories

Abstract

We give a review of the extended conformal algebras, known as $W$ algebras, which contain currents of spins higher than 2 in addition to the energy-momentum tensor. These include the non-linear $W_N$ algebras; the linear $W_\infty$ and $W_{1+\infty}$ algebras; and their super-extensions. We discuss their applications to the construction of $W$-gravity and $W$-string theories.