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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• On k-String Tensions and Domain Walls in N=1 Gluodynamics
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Cited by in corpus (233)

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• Quantum Vortex Strings: A Review
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• On the moduli space of semilocal strings and lumps
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• Color Magnetic Flux Tubes in Dense QCD
• Color Magnetic Flux Tubes in Dense QCD. II: Effective World-Sheet Theory
• Constructing Non-Abelian Vortices with Arbitrary Gauge Groups
• Cosmic strings and their induced non-Gaussianities in the cosmic microwave background
• Correspondence between Skyrmions in 2+1 and 3+1 Dimensions
• Quantization of Integrable Systems and a 2d/4d Duality
• Integrability of Vortex Equations on Riemann Surfaces
• Heterotic Flux Tubes in N=2 SQCD with N=1 Preserving Deformations
• 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
• Non-Abelian Vortices in Supersymmetric Gauge Field Theory via Direct Methods
• Large-N Solution of the Heterotic N=(0,2) Two-Dimensional CP(N-1) Model
• 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 strings and domain walls in two Higgs doublet models
• Dynamics of Domain Wall Networks
• Fractional Vortices and Lumps
• Non-Abelian Sine-Gordon Solitons
• Confined Monopoles Induced by Quantum Effects in Dense QCD
• Scalar fields and defect structures: perturbative procedure for generalized models
• Magnetic Impurity Inspired Abelian Higgs Vortices
• Chern--Simons Vortices in the Gudnason Model
• 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
• Existence of Multiple Vortices in Supersymmetric Gauge Field Theory
• The Background Field Method as a Canonical Transformation
• Magnetic strings in Lattice QCD as Nonabelian Vortices
• Topological order in a color-flavor locked phase of $(3+1)$-dimensional $U(N)$ gauge-Higgs system
• Non-Abelian Confinement in N=2 Supersymmetric QCD: Duality and Kinks on Confining Strings
• Non-Abelian Monopoles in the Higgs Phase
• Exact Kink Solitons in Skyrme Crystals
• Confined Magnetic Monopoles in Dense QCD
• Non-Abelian Chern-Simons vortices with generic gauge groups
• SO and USp Kahler and Hyper-Kahler Quotients and Lumps
• Non-Abelian Duality and Confinement in N=2 Supersymmetric QCD
• Higher Derivative Corrections to Manifestly Supersymmetric Nonlinear Realizations
• Multiple Layer Structure of Non-Abelian Vortex
• Magnetic Monopoles in Field Theory and Cosmology
• Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor
• BPS States in Omega Background and Integrability
• Non-Abelian Vortex in Four Dimensions as a Critical String on a Conifold
• Decomposing Instantons in Two Dimensions
• Solutions to the Minimization Problem Arising in a Dark Monopole Model in Gauge Field Theory
• Spontaneous Magnetization through Non-Abelian Vortex Formation in Rotating Dense Quark Matter
• Confinement of quarks and valence gluons in SU(N) Yang-Mills-Higgs models
• Fractional and semi-local non-Abelian Chern-Simons vortices
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• Dynamics of Strings between Walls
• The Dynamics of Chern-Simons Vortices
• A Matrix Model for Non-Abelian Quantum Hall States
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• Coexisting Vortices and Antivortices Generated by Dually Gauged Harmonic Maps
• The Moduli Space Metric for Well-Separated Non-Abelian Vortices
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• CP(N-1) model on finite interval in the large N limit
• Geometrically constrained kinklike configurations engendering long range, double exponential, half-compact and compact behavior
• Critical Non-Abelian Vortex in Four Dimensions and Little String Theory
• Josephson junction of non-Abelian superconductors and non-Abelian Josephson vortices
• Confinement in N=1 SQCD: One Step Beyond Seiberg's Duality
• Non-Abelian k-Vortex Dynamics in N=1^* theory and its Gravity Dual
• Manifestations of magnetic vortices in equation of state of Yang-Mills plasma
• Aharonov-Bohm Phase in High Density Quark Matter
• Non-Abelian String of a Finite Length
• Chiral Magnets from String Theory
• Dynamics of Non-Abelian Vortices
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• Topological Nambu monopole in two Higgs doublet models
• Josephson instantons and Josephson monopoles in a non-Abelian Josephson junction
• Non-Abelian Duality and Confinement: from N=2 to N=1 Supersymmetric QCD
• On the Stability of Non-Abelian Semi-local Vortices
• CP(N) sigma model on a finite interval revisited
• Casimir Force for the $\mathbb{C}{P}^{N-1}$ Model
• Hadrons of N=2 Supersymmetric QCD in Four Dimensions from Little String Theory
• Stable $Z$-strings with topological polarization in two Higgs doublet model
• Stable core symmetries and confined textures for a vortex line in a spinor Bose-Einstein condensate
• Confinement-Deconfinement Crossover in the Lattice $\mathbb{C}{P}^{N-1}$ Model
• Revisiting the Faddeev-Skyrme Model and Hopf Solitons
• Vortex counting from field theory
• Non Abelian Chern-Simons-Higgs solutions in (2+1) dimensions
• 2d Partition Function in Omega-background and Vortex/Instanton Correspondence
• Instantons confined by monopole strings
• Description of the Heterotic String Solutions in U(N) SQCD
• r Duality and "Instead-of-Confinement" Mechanism in N=1 Supersymmetric QCD
• Different faces of confinement
• Non-Abelian Vortices, Super-Yang-Mills Theory and Spin(7)-Instantons
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• Quantum corrections to the noncommutative kink
• 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
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• Large-N Solution of the Heterotic CP(N-1) Model with Twisted Masses
• Domain Wall Equations, Hessian of Superpotential, and Bogomol'nyi Bounds
• Non-Abelian Vortices with an Aharonov-Bohm Effect
• Topological first-order vortices in a gauged CP(2) model
• Non-Abelian Vortices without Dynamical Abelianization
• Non-Abelian Strings and the Luscher Term
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• Strong versus Weak Coupling Confinement in N=2 Supersymmetric QCD
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• Incarnations of Instantons
• Chiral non-Abelian vortices and their confinement in three flavor dense QCD
• Crossover between Abelian and non-Abelian confinement in N=2 supersymmetric QCD
• Vortex-Strings in N=2 SQCD and Bulk-String Decoupling
• On the Integrability of Four Dimensional N=2 Gauge Theories in the Omega Background
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Non-Abelian statistics of vortices with non-Abelian Dirac fermions
• First-order solitons with internal structures in an extended Maxwell-$CP(2)$ model
• The effective action of a BPS Alice string
• Nonabelian strings in a dense matter
• Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems
• Dyonic Non-Abelian Vortices
• Heterotic N=(0,2) CP(N-1) Model with Twisted Masses
• Higher Winding Strings and Confined Monopoles in N=2 SQCD
• Non-Abelian Vortices on the Torus
• Low-energy U(1) x USp(2M) gauge theory from simple high-energy gauge group
• 3D Dualities and Supersymmetry Enhancement from Domain Walls
• Aharonov-Bohm defects
• A Magnetic-Monopole-Based Mechanism to the formation of the Hot Big Bang Modeled Universe
• Exhausting all exact solutions of BPS domain wall networks in arbitrary dimensions
• Supersymmetry Breaking on Gauged Non-Abelian Vortices
• Non-Abelian strings in N=1 supersymmetric QCD
• Confinement and duality in supersymmetric gauge theories
• Confinement and Localization on Domain Walls
• BPS states in the Omega-background and torus knots
• Condensates and instanton - torus knot duality. Hidden Physics at UV scale
• One-loop results for kink and domain wall profiles at zero and finite temperature
• Self-consistent Analytic Solutions in Twisted $\mathbb{C}{P}^{N-1}$ Model in the Large-$N$ Limit
• Matching the linear spectra of twinlike defects
• Confining solitons in the Higgs phase of $\mathbb{C}{P}^{N-1}$ model: Self-consistent exact solutions in large-$N$ limit
• A Study of Wall-Crossing: Flavored Kinks in D=2 QED
• Comments on the NSVZ $\beta$ Functions in Two-dimensional $\mathcal{N}=(0,2)$ Supersymmetric Models
• Coleman-Weinberg Abrikosov-Nielsen-Olesen strings
• Detailing N=1 Seiberg's Duality through the Seiberg-Witten Solution of N=2
• Exact solutions of domain wall junctions in arbitrary dimensions
• Confronting Seiberg's Duality with r Duality in N=1 Supersymmetric QCD
• BPS Spectrum of Supersymmetric CP(N-1) Theory with Z_N Twisted Masses
• Exploring gauge theories with adjoint matter on the lattice
• RG limit cycles
• Hybrid r-Vacua in N=2 Supersymmetric QCD: Universal Condensate Formula
• Non-Abelian Vortex-String Dynamics from Nonlinear Realization
• Non-Abelian Yang-Mills-Higgs vortices
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• Quantum Exact Non-Abelian Vortices in Non-relativistic Theories
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• Solitonic ground state in supersymmetric theory in background
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• Zero-modes of Non-Abelian Solitons in Three Dimensional Gauge Theories
• Nontopological first-order vortices in a gauged $CP(2)$ model with a dielectric function
• Large-N Solution of the Heterotic N=(0,1) Two-Dimensional O(N) Sigma Model
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• Description of the Heterotic String Solutions in the M Model
• On The Problem of the Quantum Heterotic Vortex
• J-kink domain walls and the DBI action
• Quantum Deformation of the Effective Theory on Non-Abelian string and 2D-4D correspondence
• BPS Equations and the Stress Tensor
• BPS Boojums in N=2 supersymmetric gauge theories I
• What Becomes of Semilocal non-Abelian Strings in $\mathcal{N}=1$ Supersymmetric QCD
• Heterotic Non-Abelian String of a Finite Length
• Dynamics of non-Abelian strings in the theory interpolating from $\mathcal{N}=2$ to $\mathcal{N}=1$ supersymmetric QCD
• BPS pion domain walls in the supersymmetric chiral Lagrangian
• 2D-4D Correspondence: Towers of Kinks versus Towers of Monopoles in N=2 Theories
• Monopole-vortex complex in a theta vacuum
• Static Interactions of U(N) non-Abelian Vortices
• New Results on Non-Abelian Vortices - further insights into monopole, vortex and confinement
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• Matching 3d N=2 Vortices and Monopole Operators
• Fermion scattering on topological solitons in the ${\mathbb{CP}}^{N-1}$ model
• Quantum SUSY Algebra of $Q$-lumps in the Massive Grassmannian Sigma Model
• Extended multi-scalar field theories in (1+1) dimensions
• Topological first-order solitons in a gauged $CP(2)$ model with the Maxwell-Chern-Simons action
• Non-Abelian vortex in lattice gauge theory
• Neutrino zeromodes on electroweak strings in light of topological insulators
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• Vortex-strings in N=2 quiver X U(1) theories
• Dyonic non-Abelian vortex strings in supersymmetric and non-supersymmetric theories: tensions and higher derivative corrections
• Dual formulations of vortex strings in supersymmetric Abelian Higgs model
• String Dynamics, Spontaneous Breaking of Supersymmetry and Dual Scalar Field Theory
• Trapping of Spin-0 fields on tube-like topological defects
• Recent Progress in AdS/CFT
• NS Three-form Flux Deformation for the Critical Non-Abelian Vortex String
• Revisiting Critical Vortices in Three-Dimensional SQED
• Local and Semi-local Vortices in Yang-Mills-Chern-Simons model
• 2d Sigma Models on Non-compact Calabi-Yau and $\mathcal{N}=2$ Liouville Theory
• Confinement and moduli locking of Alice strings and monopoles
• Singular SQCD Vacua and Confinement
• Non-Abelian Vortex in Four Dimensions as a Critical Superstring
• Critical Non-Abelian Vortex String and 2D N=2 Black Hole
• Fermion-soliton scattering in a modified ${\mathbb{CP}}^1$ model
• Effective Lagrangian of Domain Wall Networks
• Nontopological first-order vortices in a gauged $CP(2)$ theory endowed with the Chern-Simons action
• Theoretical Developments in SUSY
• Chiral non-Abelian vortex molecules in dense QCD
• Kink properties in Lorentz-violating scalar field theory
• Long Way to Ricci Flatness
• BPS Boojums in N=2 supersymmetric gauge theories II
• Domain Wall and Three Dimensional Duality
• Quantizing a solitonic string
• Confining Strings in Supersymmetric Theories with Higgs Branches
• Chiral non-Abelian domain walls in the Ginzburg-Landau theory
• Large-$N$ Solution and Effective Action of "Twisted-Mass'' Deformed $\mathbb{CP}(N-1)$ Model
• Observations of 't Hooft's sublattices and Dirac's monopole by inhomogeneous phases of solitons
• Dynamics of non-Abelian strings in supersymmetric gauge theories
• Yang--Mills Monopoles in Extremal Reissner--Nordström Black Hole Metric
• Heterotically Deformed Sigma Models on the World Sheet of Semilocal Strings in SQED