Noncommutative Two Dimensional Gravities

TL;DR

This paper formulates noncommutative two-dimensional gravities using gauge theories, showing classical solutions persist from commutative to noncommutative cases, emphasizing the role of twisted diffeomorphisms.

Contribution

It introduces a gauge theory formulation of noncommutative 2D gravity and demonstrates the stability of classical solutions under noncommutative deformation.

Findings

Classical solutions of commutative theories remain valid in noncommutative versions.

Twisted diffeomorphisms are essential for maintaining solution correspondence.

The approach bridges noncommutative geometry with gravitational theories.

Abstract

We give formulations of noncommutative two dimensional gravities in terms of noncommutative gauge theories. We survey their classical solutions and show that solutions of the corresponding commutative theories continue to be solutions in the noncommutative theories as well. We argue that the existence of ``twisted'' diffeomorphisms, recently introduced in hep-th/0504183, is crucial for this conclusion.