  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.
