Three dimensional gravity and Quantum Hall Effect

TL;DR

This paper explores the connection between three-dimensional Einstein gravity with AdS geometry and the Quantum Hall Effect, demonstrating that non-commutative three-dimensional gravity is equivalent to a matrix exciton model, linking gravity and condensed matter physics.

Contribution

It establishes a novel equivalence between non-commutative 3D gravity and a matrix exciton model, integrating gravity theories with quantum Hall physics.

Findings

Non-commutative 3D gravity is equivalent to the matrix exciton model.

Gravity in AdS space can be described via Chern-Simons theory.

Quantum Hall Effect relates to non-commutative gauge theories.

Abstract

Recently three dimensional Einstein gravity with AdS geometry has been studied, and pointed out to be described with Chern-Simons theory by Grumiller and Jackiw. While, non-commutative Chern-Simons theory is known to be equivalent to Quantum Hall Effect, through Area Preserving Diffeomorphism by Susskind and others. Conbining these, three dimensional gravity is studied in this paper in the context of the Quantum Hall Effect, and non-commutative three dimensional gravity is shown to be equivalent to the matrix formulated exciton model which is the two component matrix model previously by the author.