Solitons in the Higgs phase -- the moduli matrix approach --

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).

89 pages, 33 figures, invited review article to Journal of Physics A: Mathematical and General, v3: typos corrected, references added, the published version

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• Search for NS 3-form Flux Induced Vacua for the Critical Non-Abelian Vortex String
• Chiral non-Abelian domain walls in the Ginzburg-Landau theory
• Domain Walls, The Extended Superconformal Algebra, and The Supercurrent
• Index Theorem for non-Supersymmetric Fermions Coupled to a non-Abelian String and Electric Charge Quantization
• The moduli space of non-Abelian vortices in Yang-Mills-Chern-Simons-Higgs theory
• SO and USp (Hyper)Kahler Quotients and Lumps
• Dynamics of non-Abelian strings in supersymmetric gauge theories
• Mass deformed world-sheet action of semi-local vortices
• Analytic Approach for Computation of Topological Number of Integrable Vortex on Torus
• Colliding Waves on a Brane, the Big Bounce and Reconnection
• Dynamical Realization of the Brane world Scenario Using Topological Solitons