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 by varying the Higgs VEV v. As one lowers v from the Polyakov semiclassical regime v 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 v ' g, where dynamical mass generation of a gauge-symmetric gauge-boson mass m ' g takes place, in addition to the Higgs-generated non-symmetric mass M ' vg. This dynamical mass generation is forced by the infrared instability (in both 3 and 4 dimensions) of the pure-gauge theory. We construct solitonic configurations of the theory with both m,M 6= 0 which are generically closed loops consisting of nexuses (a class of soliton recently studied for the 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 the pure-gauge M = 0 limit the homotopy Π2(SU(2)/U(1)) = Z2 (or its analog for SU(N)) of the ’t Hooft-Polyakov monopoles is no longer applicable, and is replaced by the center-vortex homotopy Π1(SU(N)/ZN ) = ZN of the center vortices. *E-mail address: [email protected] UCLA/98/TEP/37 December, 1998