What Becomes of Semilocal non-Abelian Strings in $\mathcal{N}=1$ Supersymmetric QCD

Abstract

We study non-Abelian vortex strings in $\mathcal{N}=2$ supersymmetric QCD with the gauge group U$(N)$ deformed by the mass $\mu$ of the adjoint matter. This deformation breaks $\mathcal{N}=2$ supersymmetry down to $\mathcal{N}=1$ and in the limit of large $\mu$ the theory flows to $\mathcal{N}=1$ QCD. Non-Abelian strings in addition to translational zero modes have orientation moduli. In the $\mathcal{N}=2$ limit of small $\mu$ the dynamics of orientational moduli is described by the two dimensional $CP(N-1)$ model for QCD with $N_f=N$ flavors of quark hypermultiplets. For the case of $N_f>N$ the non-Abelian string becomes semilocal developing additional size moduli which modify the effective two dimensional $\sigma$-model on the string making its target space non-compact. In this paper we consider the $\mu$-deformed theory with $N_f>N$ eventually making $\mu$ large. We show that size moduli develop a potential that forces the string transverse size to shrink. Eventually in the large $\mu$ limit size moduli decouple and the effective theory on the string reduces to the $CP(N-1)$ model. We also comment on physics of confined monopoles.

arXiv comment15 pages; minor changes introduced

References in corpus (23)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Vortices, Instantons and Branes
• Semilocal and Electroweak Strings
• Nonabelian Superconductors: Vortices and Confinement in $\mathcal{N}=2$ SQCD
• Solitons in the Higgs phase -- the moduli matrix approach --
• Vortex Strings and Four-Dimensional Gauge Dynamics
• Non-Abelian String Junctions as Confined Monopoles
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Confinement and Strings in MQCD
• Monopoles in the Higgs Phase
• Quantum Vortex Strings: A Review
• Semilocal Topological Defects
• Non-Abelian Semilocal Strings in N=2 Supersymmetric QCD
• On the moduli space of semilocal strings and lumps
• Manifestly Supersymmetric Effective Lagrangians on BPS Solitons
• Type I Superconductivity upon Monopole Condensation in Seiberg-Witten Theory
• Semilocal Defects
• Effective World-Sheet Theory for Non-Abelian Semilocal Strings in N = 2 Supersymmetric QCD
• Lessons from supersymmetry: "Instead-of-Confinement" Mechanism
• Revisiting the Faddeev-Skyrme Model and Hopf Solitons
• Description of the Heterotic String Solutions in U(N) SQCD
• Non-Abelian strings in N=1 supersymmetric QCD

Cited by in corpus (3)

• Some comments about emission channels of non abelian vortices
• Heterotically Deformed Sigma Models on the World Sheet of Semilocal Strings in SQED
• Dynamics of non-Abelian strings in supersymmetric gauge theories