Center vortices, nexuses, and the Georgi-Glashow model

In a gauge theory with no Higgs fields the mechanism for confinement is by center vortices, but in theories with adjoint Higgs fields and generic symmetry breaking, such as the Georgi-Glashow model, Polyakov showed that in d = 3 confinement arises via a condensate of 't Hooft-Polyakov monopoles. We study the connection in d = 3 between pure-gauge-theory and the theory with adjoint Higgs fields by varying the Higgs VEV upsilon. As one lowers upsilon from the Polyakov semiclassical regime upsilon much greater than g (g is the gauge coupling) toward zero, where the unbroken theory lies, one encounters effects associated with the unbroken theory at a finite value upsilon similar or equal to g, where dynamical mass generation of a gauge-symmetric gauge-boson mass m similar or equal to g(2) takes place, in addition to the Higgs-generated non-symmetric mass M similar or equal to upsilon g. This dynamical mass generation is forced by the infrared instability tin both 3 and 4 dimensions) of the pure-gauge theory. We construct solitonic configurations of the theory with both m,M not equal 0 which are generically closed loops consisting of nexuses (a class of soliton recently studiedfdlthe pure-gauge theory), each paired with an antinexus, sitting like beads on a string of center vortices with vortex fields always pointing into (out of) a nexus (antinexus); the vortex magnetic fields extend a transverse distance 1/m. An isolated nexus with vortices is continuously deformable from the 't Hooft-Polyakov (m = 0) monopole to the pure-gauge-nexus-vortex complex (M = 0). In thr pure-gauge M = 0 limit the homotopy Pi(2)(SU(2)/U(1)) = Z [or its analog for SU(N)] of the 't Hooft-Polyakov monopoles is no longer applicable, and is replaced by the center-vortex homotopy (Pi(1)(SU(N)/Z(N)) = Z(N) of the center vortices. [S0556-2821(99)06012-9].