Embedding Space Approach to JT Gravity

TL;DR

This paper introduces a coordinate-free gauge theory approach to Euclidean JT gravity, emphasizing background space construction, novel gauge features, and potential generalizations to non-commutative spaces.

Contribution

It presents a new coordinate-free gauge theory formulation of Euclidean JT gravity using Killing vectors, with a unique feature that zero field strength does not imply pure gauge, and discusses non-commutative generalizations.

Findings

Constructed a background space approach to JT gravity.

Identified solutions where the metric is induced from the background.

Proposed a non-commutative space generalization.

Abstract

We present a coordinate-free background space construction of Euclidean Jackiw-Teitelboim gravity. It is written as a gauge theory that utilizes the Killing vectors and conformal Killing vectors of a hyperboloid embedded in a three dimensional background. A novel feature of the gauge theory is that vanishing field strength does not necessarily imply that the gauge potentials are pure gauges, not even locally. As is usual, metric tensors are dynamically generated from the classical solutions of the theory, which here do not rely on coordinate charts on the two-dimensional surface. We find a special class of solutions whereby the derived metric tensor on the surface is the induced metric from the background space. The gauge theory construction given here has a natural generalization to a non-commutative space, which does not require the use of coordinates, symbols or a star product.