Non-Abelian Monopoles in the Higgs Phase
arXiv:1012.4057 · doi:10.1016/j.nuclphysb.2011.02.014
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
References in corpus (25)
- Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
- All Exact Solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield Equation
- Instantons in the Higgs Phase
- Construction of Non-Abelian Walls and Their Complete Moduli Space
- Non-Abelian Walls in Supersymmetric Gauge Theories
- Universal Reconnection of Non-Abelian Cosmic Strings
- On the moduli space of semilocal strings and lumps
- Manifestly Supersymmetric Effective Lagrangians on BPS Solitons
- Non-Abelian duality from vortex moduli: a dual model of color-confinement
- D-brane Construction for Non-Abelian Walls
- Constructing Non-Abelian Vortices with Arbitrary Gauge Groups
- Webs of Walls
- Global Structure of Moduli Space for BPS Walls
- Domain Walls with Non-Abelian Clouds
- Statistical Mechanics of Vortices from D-branes and T-duality
- Non-Abelian vortices and monopoles in SO(N) theories
- Intersecting Solitons, Amoeba and Tropical Geometry
- Non-Abelian Vortices in SO(N) and USp(N) Gauge Theories
- Non-Abelian vortex dynamics: Effective world-sheet action
- Effective Action of Domain Wall Networks
- Static Interactions of non-Abelian Vortices
- Group Theory of Non-Abelian Vortices
- On the Stability of Non-Abelian Semi-local Vortices
- Magnetic Charge Lattices, Moduli Spaces and Fusion Rules
- Monopole-charge instability