Solitons in the Higgs phase: The Moduli matrix approach
Feb, 2006
89 pages
Published in:
- J.Phys.A 39 (2006) R315-R392
e-Print:
- hep-th/0602170 [hep-th]
Report number:
- TIT-HEP-550
View in:
Citations per year
Abstract:
We review our recent work on solitons in the Higgs phase. We use U(N_C) gauge theory with N_F Higgs scalar fields in the fundamental representation, which can be extended to possess eight supercharges. We propose the moduli matrix as a fundamental tool to exhaust all BPS solutions, and to characterize all possible moduli parameters. Moduli spaces of domain walls (kinks) and vortices, which are the only elementary solitons in the Higgs phase, are found in terms of the moduli matrix. Stable monopoles and instantons can exist in the Higgs phase if they are attached by vortices to form composite solitons. The moduli spaces of these composite solitons are also worked out in terms of the moduli matrix. Webs of walls can also be formed with characteristic difference between Abelian and non-Abelian gauge theories. We characterize the total moduli space of these elementary as well as composite solitons. Effective Lagrangians are constructed on walls and vortices in a compact form. We also present several new results on interactions of various solitons, such as monopoles, vortices, and walls. Review parts contain our works on domain walls (hep-th/0404198, hep-th/0405194, hep-th/0412024, hep-th/0503033, hep-th/0505136), vortices (hep-th/0511088, hep-th/0601181), domain wall webs (hep-th/0506135, hep-th/0508241, hep-th/0509127), monopole-vortex-wall systems (hep-th/0405129, hep-th/0501207), instanton-vortex systems (hep-th/0412048), effective Lagrangian on walls and vortices (hep-th/0602289), classification of BPS equations (hep-th/0506257), and Skyrmions (hep-th/0508130).Note:
- 89 pages, 33 figures, invited review article to Journal of Physics A: Mathematical and General, v3: typos corrected, references added, the published version Report-no: TIT/HEP-550 Subj-class: High Energy Physics - Theory: Differential Geometry: Pattern Formation and Solitons Journal-ref: J.Phys. A39 (2006) R315-R392 DOI: 10.1088/0305-4470/39/26/R01
- 11.15.-q
- 05.45.Yv
- 11.10.Lm
- 11.25.-w
- review
- gauge field theory: U(N)
- Higgs model
- Higgs particle: flavor
- soliton: BPS
- charge: topological
References(173)
Figures(0)