New solutions for non-Abelian cosmic strings (1607.00764v2)

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, including SO(10). We argue that semipoles and supercurrents are generic on GUT strings.

• The paper identifies new semipole solutions emerging from SU(2) symmetry breaking in non-Abelian cosmic strings.
• It employs theoretical modeling and numerical simulations to reveal complex magnetic fluxes and discrete charge phenomena.
• The findings enhance our understanding of cosmic string stability and imply significant roles in Grand Unified Theories.

An Analytical Exploration of Non-Abelian Cosmic String Solutions

The paper "New solutions for non-Abelian cosmic strings" presents an intricate analysis of classical vortex solutions in a non-Abelian gauge theory, investigating their emergent properties when embedded within various symmetry frameworks. The paper is situated in the context of non-Abelian gauge theories, specifically focusing on the $\mathrm{SU}(2)$ gauge symmetry and its breakdown to discrete symmetries, creating cosmic string solutions with intriguing physical characteristics.

Study Objective and Approach

The primary objective of the analysis is to explore the behavior of cosmic strings arising due to the breakdown of $\mathrm{SU}(2)$ gauge symmetry in the presence of two adjoint Higgs fields. These cosmic strings, which are line-like topological defects, are of significant interest in theoretical physics for their potential implications in Grand Unified Theories (GUTs) and their cosmological roles. The research utilizes theoretical modeling and numerical simulations to identify new types of monopole structures on cosmic strings, dubbed "semipoles," which emerge due to the spontaneous breakdown of discrete symmetries in the theory.

Key Findings and Numerical Results

The major contribution of this paper lies in the identification and analysis of new vortex-like solutions, particularly semipoles, which were not anticipated in previous explorations of similar systems. These semipoles manifest under conditions where the gauge symmetry is reduced by the presence of degenerate Higgs mass states, aligning with a heightened discrete $Z_4$ symmetry. Each semipole represents a kink solution interpolating between string solutions, characterized by complex magnetic fluxes and discrete charges. Numerical simulations confirm the model's predictions, illustrating configurations where these semipoles act as sources for a complex gauge invariant magnetic flux, coordinating between four degenerate string solutions.

The elegance of these solutions is visible in the quantification of strings bearing supercurrents, which appear when symmetry becomes continuous—attributable to specific values of the Higgs self-couplings. These supercurrents suggest persistent global currents analogous to those observed in superfluid states.

Theoretical and Practical Implications

The paper advances the theoretical understanding of cosmic strings within the framework of non-Abelian gauge theories and GUTs. By embedding the discussed $\mathrm{SU}(2)$ system in the broader context of GUTs like $\mathrm{SO}(10)$, the results suggest that semipoles and superfluid characteristics of cosmic strings may be universal among high-energy scales. This establishes a potential for cosmic strings to engage with fundamental cosmological phenomena, including the dynamics of the early universe and prospective observational signatures.

Moreover, the existence of these features—semipoles and supercurrents—induces possible stabilizing mechanisms against string collapse, which could lead to metastable cosmic effects with significant implications for current understanding and future explorations in cosmic string research.

Conclusions and Future Directions

The conclusions of this paper bring to light the nuanced and intricate structure of cosmic strings as influenced by discrete and continuous symmetry breakings. This revelation of semipole solutions adds a substantive layer to the topological and energetic characteristics of cosmic strings in non-Abelian gauge frameworks, illustrating both their complexity and potential ubiquity across theoretical extensions of the Standard Model.

Looking forward, the ongoing challenge remains to integrate these theoretical constructs into verifiable observational phenomena and cosmological models, potentially through astronomical observations of cosmic string-induced perturbations or by refining numerical simulations to explore their cosmological consequences in greater detail. Further exploration into varying parameter regimes and couplings within GUT frameworks is likely to yield additional insights, expanding on the foundational aspects laid out in this paper.