Confinement and moduli locking of Alice strings and monopoles

Abstract

We argue that strings (vortices) and monopoles are confined, when fields receiving nontrivial Aharonov-Bohm (AB) phases around a string develop vacuum expectation values (VEVs). We illustrate this in an $SU(2)\times U(1)$ gauge theory with charged triplet complex scalar fields admitting Alice strings and monopoles, by introducing charged doublet scalar fields receiving nontrivial AB phases around the Alice string. The Alice string carries a half $U(1)$ magnetic flux and $1/4$ $SU(2)$ magnetic flux taking a value in two of the $SU(2)$ generators characterizing the $U(1)$ modulus. This string is not confined in the absence of a doublet VEV in the sense that the $SU(2)$ magnetic flux can be detected at large distance by an AB phase around the string. When the doublet field develops VEVs, there appear two kinds of phases that we call deconfined and confined phases. When a single Alice string is present in the deconfined phase, the $U(1)$ modulus of the string and the vacuum moduli are locked (the bulk-soliton moduli locking). In the confined phase, the Alice string is inevitably attached by a domain wall that we call an AB defect and is confined with an anti-Alice string or another Alice string with the same $SU(2)$ flux. Depending on the partner, the pair annihilates or forms a stable doubly-wound Alice string having an $SU(2)$ magnetic flux inside the core, whose color cannot be detected at large distance by AB phases, implying the "color" confinement. The theory also admits stable Abrikosov-Nielsen-Olesen string and a ${\mathbb{Z}}_2$ string in the absence of the doublet VEVs, and each decays into two Alice strings in the presence of the doublet VEVs. A monopole in this theory can be constructed as a closed Alice string with the $U(1)$ modulus twisted once, and we show that with the doublet VEVs, monopoles are also confined to monopole mesons of the monopole charge two.

arXiv comment36 pages, 10 figures

References in corpus (40)

• Spinor Bose-Einstein condensates
• Nonabelian Superconductors: Vortices and Confinement in $\mathcal{N}=2$ SQCD
• Solitons in the Higgs phase -- the moduli matrix approach --
• Axions : Theory and Cosmological Role
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Moduli Space of Non-Abelian Vortices
• Instantons in the Higgs Phase
• Knots in a Spinor Bose-Einstein Condensate
• How to create Alice string (half-quantum vortex) in a vector Bose-Einstein condensate
• Non-Abelian Vortices of Higher Winding Numbers
• Semi-superfluid strings in High Density QCD
• Quantum Field Theory of Nonabelian Strings and Vortices
• Monopole core instability and Alice rings in spinor Bose-Einstein condensates
• Non-Abelian Strings in High Density QCD: Zero Modes and Interactions
• Non-abelian vortices and non-abelian statistics
• Instabilities of Non-Abelian Vortices in Dense QCD
• Color Magnetic Flux Tubes in Dense QCD
• Color Magnetic Flux Tubes in Dense QCD. II: Effective World-Sheet Theory
• Open Heterotic Strings
• Internal Frame Dragging and a Global Analog of the Aharonov-Bohm Effect
• Josephson vortices and the Atiyah-Manton construction
• Jewels on a wall ring
• Quark-hadron continuity beyond Ginzburg-Landau paradigm
• Gauge/gravity duality with a chiral N=(0,8) string defect
• Anyonic particle-vortex statistics and the nature of dense quark matter
• Localized modes at a D-brane--O-plane intersection and heterotic Alice strings
• Constraints on two Higgs doublet models from domain walls
• Non-Abelian strings and domain walls in two Higgs doublet models
• Quark-hadron continuity under rotation: Vortex continuity or boojum?
• Abe homotopy classification of topological excitations under the topological influence of vortices
• Aharonov-Bohm Phase in High Density Quark Matter
• Note on a solution to domain wall problem with the Lazarides-Shafi mechanism in axion dark matter models
• On a core instability of 't Hooft Polyakov monopoles
• Non-Abelian Alice strings in two-flavor dense QCD
• Solitonic spin-liquid state due to the violation of the Lifshitz condition in Fe${}_{1+y}$Te
• SO(10) Cosmic Strings and SU(3) Color Cheshire Charge
• Topological Defects in the Georgi-Machacek Model
• More on core instabilities of magnetic monopoles
• Topologically Alice Strings and Monopoles
• Aharonov-Bohm defects

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