Black hole as topological insulator (II): the boundary modes

TL;DR

This paper explores the boundary modes of black holes, proposing that higher-dimensional black holes can support boundary fields similar to topological insulators, extending previous findings from 3D cases.

Contribution

It demonstrates that 3+1D black hole horizons can support boundary scalar and vector fields, enabling the construction of a Dirac field akin to topological insulator boundary states.

Findings

Boundary BF theory describes black hole boundary degrees of freedom.

3+1D black holes support massless scalar and vector boundary fields.

These boundary fields can form a Dirac field via bosonization.

Abstract

In the previous paper Ref.[1], it was claimed that the black hole can be considered as a kind of topological insulator. For BTZ black hole in three dimensional $AdS_3$ spacetime two evidences were given to support this claim: the first evidence comes from the black hole "membrane paradigm", and the second evidence comes from the fact that the horizon of BTZ black hole can support two chiral massless scalar field with opposite chirality. Those are two key properties of 2D topological insulator. For higher dimensional black hole the first evidence is still valid but the second fails. In this paper, starting from the boundary BF theory, which can be used to describe the boundary degrees of freedom of black hole in arbitrary dimension, we shown that the isolated horizon of $3+1-$D black hole can support massless scalar field and vector field. Those two fields can be used to construct a massless Dirac field through the $2+1-$dimensional bosonization, which also appears on the boundary of $3+1-$D topological insulators.