Nonabelian Superconductors: Vortices and Confinement in $\mathcal{N}=2$ SQCD

Abstract

We study nonabelian vortices (flux tubes) in SU(N) gauge theories, which are responsible for the confinement of (nonabelian) magnetic monopoles. In particular a detailed analysis is given of $\mathcal{N}=2$ SQCD with gauge group SU(3) deformed by a small adjoint chiral multiplet mass. Tuning the bare quark masses (which we take to be large) to a common value $m$, we consider a particular vacuum of this theory in which an SU(2) subgroup of the gauge group remains unbroken. We consider $5\ge N_f\ge 4$ flavors so that the SU(2) sub-sector remains non asymptotically free: the vortices carrying nonabelian fluxes may be reliably studied in a semi-classical regime. We show that the vortices indeed acquire exact zero modes which generate global rotations of the flux in an $SU(2{)}_{C+F}$ group. We study an effective world-sheet theory of these orientational zero modes which reduces to an $\mathcal{N}=2$ O(3) sigma model in (1+1) dimensions. Mirror symmetry then teaches us that the dual SU(2) group is not dynamically broken.

37 pages Latex, 6 eps figures, Typos corrected and a few sentences added or corrected

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• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Simple Singularities and N=2 Supersymmetric Yang-Mills Theory
• The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory
• Semilocal and Electroweak Strings
• The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD
• The Coulomb Phase of N=2 Supersymmetric QCD
• Dynamics of $SU(N)$ Supersymmetric Gauge Theory
• On the Quantum Moduli Space of Vacua of $N=2$ Supersymmetric $SU(N_c)$ Gauge Theories
• Nonperturbative Effective Actions of N=2 Supersymmetric Gauge Theories
• Confinement and Strings in MQCD
• The Vacuum Structure of N=2 SuperQCD with Classical Gauge Groups
• On the Quantum Moduli Space of N=2 Supersymmetric Gauge Theories
• Domain Walls and Flux Tubes in N=2 SQCD: D-Brane Prototypes
• More on the Tensorial Central Charges in N=1 Supersymmetric Gauge Theories (BPS Wall Junctions and Strings)
• The BPS Spectra and Superconformal Points in Massive N=2 Supersymmetric QCD
• Dynamical Symmetry Breaking in Supersymmetric SU(n_c) and USp(2n_c) Gauge Theories
• Type I Superconductivity upon Monopole Condensation in Seiberg-Witten Theory
• Massive and massless monopoles with nonabelian magnetic charges
• Messages for QCD from the Superworld
• BPS String Solutions in Non-Abelian Yang-Mills Theories and Confinement
• Non-Abelian Confinement via Abelian Flux Tubes in Softly Broken N=2 SUSY QCD
• Metastable Strings in Abelian Higgs Models Embedded in Non-Abelian Theories: Calculating the Decay Rate
• Vortices on the Higgs Branch of the Seiberg-Witten Theory
• Non-Abelian Vortex and Confinement
• Dynamics of Supersymmetric SU(n_c) and USp(2n_c) Gauge Theories
• Phases of dual superconductivity and confinement in softly broken N=2 supersymmetric Yang-Mills theories
• Vacuum Structure and Flavor Symmetry Breaking in Supersymmetric SO(n_c) Gauge Theories
• Z_3 Strings and their Interactions
• Isomonodromic Properties of the Seiberg-Witten Solution
• New vortex solution in SU(3) gauge-Higgs theory
• Flux Tubes on Higgs Branches in SUSY Gauge Theories
• Non Abelian Magnetic Monopoles and Dynamics of Confinement
• Almost Conformal Vacua and Confinement

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