  We introduce (generalised) Pfaffian operators into our lattice calculations
of the mass spectra and confining string tensions of SO(2N) gauge theories,
complementing the conventional trace operators used in previous lattice
calculations. In SO(6) the corresponding `Pfaffian' particles match the
negative charge conjugation particles of SU(4), thus resolving a puzzle arising
from the observation that SO(6) and SU(4) have the same Lie algebra. The same
holds true (but much more trivially) for SO(2) and U(1). For SO(4) the Pfaffian
particles are degenerate with, but orthogonal to, those obtained with the usual
single trace operators. That is to say, there is a doubling of the spectrum, as
one might expect given that the Lie algebra of SO(4) is the same as that of
SU(2)xSU(2). Additional SO(8) and SO(10) calculations of the Pfaffian spectrum
confirm the naive expectation that these masses increase with N, so that they
cease to play a role in the physics of SO(N) gauge theories as N-->oo. We also
calculate the energies of Pfaffian `strings' in these gauge theories. Although
all our lattice calculations are for gauge theories in D=2+1, similar
conclusions should hold for D=3+1.
