  We investigate whether one can observe in SO(3) and SO(4) (lattice) gauge
theories the presence of spinorial flux tubes, i.e. ones that correspond to the
fundamental representation of SU(2); and similarly for SO(6) and SU(4). We do
so by calculating the finite volume dependence of the JP=2+ glueball in 2+1
dimensions, using lattice simulations. We show how this provides strong
evidence that these SO(N) gauge theories contain states that are composed of
pairs of (conjugate) winding spinorial flux tubes, i.e. ones that are in the
(anti)fundamental of the corresponding SU(N') gauge theories. Moreover, these
two flux tubes can be arbitrarily far apart. This is so despite the fact that
the fields that are available in the SO(N) lattice field theories do not appear
to allow us to construct operators that project onto single spinorial flux
tubes.
