Two-Dimensional Gravity and Nonlinear Gauge Theory

TL;DR

This paper introduces a novel gauge theory framework based on nonlinear Lie algebras to describe two-dimensional gravity, extending traditional gauge theories and exploring models with torsion, dilaton fields, and supersymmetry.

Contribution

It develops a new approach to gauge theory using nonlinear Lie algebras, providing a Yang-Mills-like formulation of 2D gravity derived from nonlinear Poincaré algebra.

Findings

Formulation of 2D gravity from nonlinear Poincaré algebra

Analysis of $R^2$ gravity with torsion

Discussion of supersymmetric extensions

Abstract

We review nonlinear gauge theory and its application to two-dimensional gravity. We construct a gauge theory based on nonlinear Lie algebras, which is an extension of the usual gauge theory based on Lie algebras. It is a new approach to generalization of the gauge theory. The two-dimensional gravity is derived from nonlinear Poincar{\' e} algebra, which is the new Yang-Mills like formulation of the gravitational theory. As typical examples, we investigate $R^2$ gravity with dynamical torsion and generic form of 'dilaton' gravity. The supersymmetric extension of this theory is also discussed.