Pfaffian particles and strings in SO(2N) gauge theories

Abstract

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) × SU(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 → ∞. 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.

Spinorial flux tubes in SO(N) gauge theories in 2+1 dimensions

“…It is interesting to understand how this can be consistent with the apparent absence of single-particle C = − states. This is a question that turns out to have a simple solution, as we have shown very recently in [5], although it is not clear at this stage whether the methods developed in that paper will be useful in helping to resolve the puzzle that is the topic of the present paper.…”