New Solutions for Non-Abelian Cosmic Strings

Abstract

We study the properties of classical vortex solutions in a non-Abelian gauge theory. A system of two adjoint Higgs fields breaks the SU(2) gauge symmetry to Z_{2}, producing 't Hooft-Polyakov monopoles trapped on cosmic strings, termed beads; there are two charges of monopole and two degenerate string solutions. The strings break an accidental discrete Z_{2} symmetry of the theory, explaining the degeneracy of the ground state. Further symmetries of the model, not previously appreciated, emerge when the masses of the two adjoint Higgs fields are degenerate. The breaking of the enlarged discrete symmetry gives rise to additional string solutions and splits the monopoles into four types of "semipole": kink solutions that interpolate between the string solutions, classified by a complex gauge-invariant magnetic flux and a Z_{4} charge. At special values of the Higgs self-couplings, the accidental symmetry broken by the string is continuous, giving rise to supercurrents on the strings. The SU(2) theory can be embedded in a wide class of grand unified theories (GUTs), including SO(10). We argue that semipoles and supercurrents are generic on GUT strings.

Scaling from gauge and scalar radiation in Abelian-Higgs string networks

“…The next simplest is an SU(2) gauge theory with two adjoint scalars, which has recently been studied numerically for the first time [33,34].…”

Vortices in a Generalized Maxwell-Higgs Model with Visible and Hidden Sectors

“…We are also thinking of enlarging the model to accommodate other symmetries, such as the SU (2) × U (1) symmetry, to explore the presence of solutions within the non-Abelian context examined before in [35], and also the SU (3) × U (1) symmetry, to investigate color-magnetic structures in the dense quark matter scenario explored recently in [56]. The presence of non-Abelian symmetries makes the problem much harder, so the search for first order differential equations that solve the equations of motion is of current interest and would be welcome.…”

Stable finite energy global vortices and asymptotic freedom

“…By integrating it, we get the value E = π, which matches with the value obtained through Eq. (12). We emphasize that the model engenders scale invariance, and this is the price we had to pay: we found stable finite energy global vortices, but we cannot decide on its size.…”

“…Then, the energy is given by Eq. (12), which leads to E = π. Therefore, even though the permittivity is negative, the energy of the system is positive.…”