Non-Abelian Monopoles in the Higgs Phase

Abstract

We use the moduli matrix approach to study the moduli space of 1/4 BPS kinks supported by vortices in the Higgs phase of N = 2 supersymmetric U(N) gauge theories when non-zero masses for the matter hypermultiplets are introduced. We focus on the case of degenerate masses. In these special cases vortices acquire new orientational degrees of freedom, and become "non-Abelian". Kinks acquire new degrees of freedom too, and we will refer to them as "non-Abelian". As already noticed for the Abelian case, non-Abelian kinks must correspond to non-Abelian monopoles of the unbroken phase of SU(N) Yang-Mills. We show, in some special cases, that the moduli spaces of the two objects are in one-to-one correspondence. We argue that the corre- spondence holds in the most general case. The consequence of our result is two-fold. First, it gives an alternative way to construct non-Abelian monopoles, in addition to other well- known techniques (Nahm transform, spectral curves, rational maps). Second, it opens the way to the study of the quantum physics of non- Abelian monopoles, by considering the simpler non-Abelian kinks.

37 pages, no figures; v2: refs. added

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• Incarnations of Skyrmions
• Effective World-Sheet Theory for Non-Abelian Semilocal Strings in N = 2 Supersymmetric QCD
• Non-Abelian Sine-Gordon Solitons: Correspondence between $SU(N)$ Skyrmions and $\mathbb{C}{P}^{N-1}$ Lumps
• Vortices and Monopoles in Mass-deformed SO and USp Gauge Theories
• Relations among topological solitons
• Topological order in a color-flavor locked phase of $(3+1)$-dimensional $U(N)$ gauge-Higgs system
• Decomposing Instantons in Two Dimensions
• Dynamics of Non-Abelian Vortices
• Josephson instantons and Josephson monopoles in a non-Abelian Josephson junction
• Stable core symmetries and confined textures for a vortex line in a spinor Bose-Einstein condensate
• Instantons confined by monopole strings
• 2d Partition Function in Omega-background and Vortex/Instanton Correspondence
• Topological Defects in the Georgi-Machacek Model
• Non-Abelian Vortices with an Aharonov-Bohm Effect
• Monopole-vortex complex at large distances and nonAbelian duality
• More on the Abrikosov Strings with Non-Abelian Moduli
• Incarnations of Instantons
• Aharonov-Bohm defects
• Degeneracy between Abelian and Non-Abelian Strings
• Effective Action of Non-Abelian Monopole-Vortex Complex
• Dynamics of slender monopoles and anti-monopoles in non-Abelian superconductor
• Quantum Energies and Tensorial Central Charges of Confined Monopoles
• BPS Boojums in N=2 supersymmetric gauge theories I
• Dual formulations of vortex strings in supersymmetric Abelian Higgs model
• Vortices and Monopoles in a Harmonic Trap
• BPS Boojums in N=2 supersymmetric gauge theories II