Wilson Loops and Black Holes in 2+1 Dimensions

TL;DR

This paper demonstrates how Wilson loops in 2+1 dimensional Chern-Simons gravity can reproduce the BTZ black hole geometry by identifying points in a four-dimensional invariant space.

Contribution

It shows a novel connection between Wilson loops in Chern-Simons theory and the geometric structure of BTZ black holes in 2+1 dimensions.

Findings

Wilson loops reproduce BTZ black hole geometry

Identification of points in invariant space models black holes

Provides a geometric interpretation of black holes via gauge theory

Abstract

In 2+1 dimensional Chern-Simons gravity, Wilson loops in the three dimensional Anti de Sitter group, $SO(2,2)$, reproduce the spinning black hole of Ba\~nados, Teitelboim and Zanelli (BTZ) by naturally duplicating the necessary identification of points of a four dimensional globally $SO(2,2)$ invariant space in which the hole appears as an embedding.