Extensions of 2D Gravity

TL;DR

This paper explores a broad class of extensions to two-dimensional gravity derived from non-trivial embeddings of sl(2) into semi-simple Lie algebras, using gauged WZW models to construct the effective action.

Contribution

It introduces a new framework for extending 2D gravity via algebraic embeddings and provides explicit formulations of the resulting effective actions.

Findings

Identifies a large class of 2D gravity extensions from algebra embeddings.

Constructs the induced action as a gauged WZW model.

Provides an exact expression for the effective action.

Abstract

After reviewing some aspects of gravity in two dimensions, it is shown that non-trivial embeddings of sl(2) in a semi-simple (super) Lie algebra give rise to a very large class of extensions of 2D gravity. The induced action is constructed as a gauged WZW model and an exact expression for the effective action is given. (Talk presented at the Journees Relativistes '93, Brussels, April, 1993).