  We study the holographic dual of the simplest notion of spin in a $p$-adic
field theory, namely Green's functions which involve non-trivial sign
characters over the $p$-adic numbers. In order to recover these sign characters
from bulk constructions, we find that we must introduce a non-dynamical $U(1)$
gauge field on the line graph of the Bruhat-Tits tree. Wilson lines of this
gauge field on suitable paths yield the desired sign characters. We show
explicitly how to start with complex scalars or fermions in the bulk, coupled
to the $U(1)$ gauge field, and compute the holographic two-point functions of
their dual operators on the boundary.
