Compact Chiral Boson Fields on the Horizon of BTZ Black Hole

TL;DR

This paper demonstrates that the horizon degrees of freedom of BTZ black holes can be modeled by compact chiral boson fields, leading to quantized black hole radii and a classification scheme via algebraic structures.

Contribution

It introduces the compactness of chiral boson fields on the horizon, resulting in quantized black hole radii and a full algebraic classification of BTZ black holes.

Findings

Quantization of the black hole radius due to compact boson fields

Construction of two abelian Kac-Moody algebras from boson fields

Full $W_{1+ abla}$ algebra used for black hole classification

Abstract

In the previous work, it was shown that the degrees of freedom on the horizon of BTZ black hole can be described by two chiral massless scalar fields with opposite chirality. In this paper, we continuous this research. It is found that the scalar field is actually a compact boson field on a circle. The compactness results in the quantization of the black hole radius. Then we quantize the two boson fields and get two abelian Kac-Moody algebras. From the boson field, one can construct the full $W_{1+\infty}$ algebra which was used to classify the BTZ black holes.