# The Conformal Field Theory on the Horizon of BTZ Black Hole

## TL;DR

This paper demonstrates that under specific boundary conditions, the boundary conformal field theory of a BTZ black hole reduces to a simple massless scalar field on its horizon, linking gravity and conformal field theories.

## Contribution

It shows how the boundary WZW theory for BTZ black holes simplifies to a massless scalar field on the horizon under certain boundary conditions.

## Key findings

- WZW theory reduces to a massless scalar field on the horizon.
- Boundary conditions are crucial for the reduction.
- Provides insight into the holographic nature of black holes.

## Abstract

In three dimensional spacetime with negative cosmology constant, the general relativity can be written as two copies of SO$(2,1)$ Chern-Simons theory. On a manifold with boundary the Chern-Simons theory induces a conformal field theory--WZW theory on the boundary. In this paper, it is show that with suitable boundary condition for BTZ black hole, the WZW theory can reduce to a massless scalar field on the horizon.