  After a review of exotic statistics for point particles in 3d BF theory, and
especially 3d quantum gravity, we show that string-like defects in 4d BF theory
obey exotic statistics governed by the 'loop braid group'. This group has a set
of generators that switch two strings just as one would normally switch point
particles, but also a set of generators that switch two strings by passing one
through the other. The first set generates a copy of the symmetric group, while
the second generates a copy of the braid group. Thanks to recent work of
Xiao-Song Lin, we can give a presentation of the whole loop braid group, which
turns out to be isomorphic to the 'braid permutation group' of Fenn, Rimanyi
and Rourke. In the context 4d BF theory this group naturally acts on the moduli
space of flat G-bundles on the complement of a collection of unlinked unknotted
circles in R^3. When G is unimodular, this gives a unitary representation of
the loop braid group. We also discuss 'quandle field theory', in which the
gauge group G is replaced by a quandle.
