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

Abstract

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.