Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories

Abstract

In the last decade it became clear that methods and techniques based on supersymmetry provide deep insights in quantum chromodynamics and other supersymmetric and non-supersymmetric gauge theories at strong coupling. In this review we summarize major advances in the critical (Bogomol'nyi-Prasad-Sommerfeld-saturated, BPS for short) solitons in supersymmetric theories and their implications for understanding basic dynamical regularities of non-supersymmetric theories. After a brief introduction in the theory of critical solitons (including a historical introduction) we focus on three topics: (i) non-Abelian strings in N=2 and confined monopoles; (ii) reducing the level of supersymmetry; and (iii) domain walls as D brane prototypes.

239 pages, 27 figures. A part of this review will be published in Rev. Mod. Phys. Comments and suggestions welcome

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• Universal Reconnection of Non-Abelian Cosmic Strings
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• Webs of Walls
• Global Structure of Moduli Space for BPS Walls
• Effective Action of Domain Wall Networks
• Central Charge Anomalies in 2D Sigma Models with Twisted Mass
• Superconformal Vortex Strings

Cited by in corpus (109)

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• Constructing Non-Abelian Vortices with Arbitrary Gauge Groups
• Correspondence between Skyrmions in 2+1 and 3+1 Dimensions
• Integrability of Vortex Equations on Riemann Surfaces
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Incarnations of Skyrmions
• Domain Walls with Non-Abelian Clouds
• BPS States in Supersymmetric Chiral Models with Higher Derivative Terms
• Effective World-Sheet Theory for Non-Abelian Semilocal Strings in N = 2 Supersymmetric QCD
• Intersecting Solitons, Amoeba and Tropical Geometry
• Non-Abelian Vortices on Riemann Surfaces: an Integrable Case
• Non-Abelian Vortices in SO(N) and USp(N) Gauge Theories
• Non-Abelian Sine-Gordon Solitons
• Fractional Vortices and Lumps
• Confined Monopoles Induced by Quantum Effects in Dense QCD
• Double-winding Wilson loops and monopole confinement mechanisms
• Non-Abelian Sine-Gordon Solitons: Correspondence between $SU(N)$ Skyrmions and $\mathbb{C}{P}^{N-1}$ Lumps
• Magnetic strings in Lattice QCD as Nonabelian Vortices
• Non-Abelian Confinement in N=2 Supersymmetric QCD: Duality and Kinks on Confining Strings
• Non-Abelian Monopoles in the Higgs Phase
• Confined Magnetic Monopoles in Dense QCD
• Higher Derivative Corrections to Manifestly Supersymmetric Nonlinear Realizations
• Non-Abelian Chern-Simons vortices with generic gauge groups
• Magnetic Monopoles in Field Theory and Cosmology
• BPS States in Omega Background and Integrability
• Confinement of quarks and valence gluons in SU(N) Yang-Mills-Higgs models
• Topological Interactions of Non-Abelian Vortices with Quasi-Particles in High Density QCD
• Fractional and semi-local non-Abelian Chern-Simons vortices
• Dynamics of Strings between Walls
• The Dynamics of Chern-Simons Vortices
• Lessons from supersymmetry: "Instead-of-Confinement" Mechanism
• Static Interactions of non-Abelian Vortices
• The Moduli Space Metric for Well-Separated Non-Abelian Vortices
• Quantum nucleation of topological solitons
• Geometrically constrained kinklike configurations engendering long range, double exponential, half-compact and compact behavior
• CP(N-1) model on finite interval in the large N limit
• Non-Abelian String of a Finite Length
• Manifestations of magnetic vortices in equation of state of Yang-Mills plasma
• Self-Consistent Large-$N$ Analytical Solutions of Inhomogneous Condensates in Quantum $\mathbb{C}{P}^{N-1}$ Model
• Chiral Magnets from String Theory
• Non-Abelian Duality and Confinement: from N=2 to N=1 Supersymmetric QCD
• On the Stability of Non-Abelian Semi-local Vortices
• Stable $Z$-strings with topological polarization in two Higgs doublet model
• Vortex counting from field theory
• Non Abelian Chern-Simons-Higgs solutions in (2+1) dimensions
• Instantons confined by monopole strings
• Different faces of confinement
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• Quantum corrections to the noncommutative kink
• D-brane solitons in various dimensions
• Non-Abelian Quasi-Gapless Modes Localized on Mass Vortices in Superfluid 3He-B
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Monopoles and Modifications of Bundles over Elliptic Curves
• String "Baryon'' in Four-Dimensional $\mathcal{N}=2$ Supersymmetric QCD from 2D-4D Correspondence
• Topological first-order vortices in a gauged CP(2) model
• Chiral non-Abelian vortices and their confinement in three flavor dense QCD
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• The effective action of a BPS Alice string
• First-order solitons with internal structures in an extended Maxwell-$CP(2)$ model
• Non-Abelian Vortices on the Torus
• Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems
• Low-energy U(1) x USp(2M) gauge theory from simple high-energy gauge group
• Nonabelian strings in a dense matter
• Dyonic Non-Abelian Vortices
• Supersymmetry Breaking on Gauged Non-Abelian Vortices
• One-loop results for kink and domain wall profiles at zero and finite temperature
• Coleman-Weinberg Abrikosov-Nielsen-Olesen strings
• Comments on the NSVZ $\beta$ Functions in Two-dimensional $\mathcal{N}=(0,2)$ Supersymmetric Models
• Exploring gauge theories with adjoint matter on the lattice
• N=1 Duality in the Chiral Limit from N=2 Duality
• Exact kink solitons in a monopole confinement problem
• First-order vortices in a gauged $CP(2)$ model with a Chern-Simons term
• Solitonic ground state in supersymmetric theory in background
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• Effective Action of Non-Abelian Monopole-Vortex Complex
• Zero-modes of Non-Abelian Solitons in Three Dimensional Gauge Theories
• Dynamics of slender monopoles and anti-monopoles in non-Abelian superconductor
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• String Dynamics, Spontaneous Breaking of Supersymmetry and Dual Scalar Field Theory
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• Kink properties in Lorentz-violating scalar field theory
• Fermion-soliton scattering in a modified ${\mathbb{CP}}^1$ model
• Theoretical Developments in SUSY
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• Critical Non-Abelian Vortex String and 2D N=2 Black Hole
• Yang--Mills Monopoles in Extremal Reissner--Nordström Black Hole Metric
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• Dynamics of non-Abelian strings in supersymmetric gauge theories
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