BTZ black hole and quantum Hall effect in the bulk/boundary dynamics

TL;DR

This paper draws an analogy between BTZ black holes and the quantum Hall effect, showing that similar effective theories describe both and connecting black hole information bounds with quantum Hall edge states.

Contribution

It establishes a novel analogy between black hole physics and quantum Hall systems using effective Chern-Simons and Liouville theories, linking bulk-boundary dynamics.

Findings

Effective Chern-Simons/Liouville description for BTZ black holes and QHE.

Bulk/UV and boundary/IR connection analogous to black hole information bounds.

Inflow of conformal and chiral anomalies corresponds to Hall current effects.

Abstract

We point out an interesting analogy between the BTZ black hole and QHE (Quantum Hall effect) in the (2+1)-dimensional bulk/boundary theories. It is shown that the Chern-Simons/Liouville(Chern-Simons/chiral boson) is an effective description for the BTZ black hole (QHE). Also the IR(bulk)-UV(boundary) connection for a black hole information bound is realized as the UV(low-lying excitations on bulk)-IR(long-range excitations on boundary) connection in the QHE. An inflow of conformal anomaly($c=1$ central charge) onto the timelike boundary of AdS$_3$ by the Noether current corresponds to an inflow of chiral anomaly onto the edge of disk by the Hall current.