Instantons in the Higgs Phase

Abstract

When instantons are put into the Higgs phase, vortices are attached to instantons. We construct such composite solitons as 1/4 BPS states in five-dimensional supersymmetric U(Nc) gauge theory with Nf(>=Nc) fundamental hypermultiplets. We solve the hypermultiplet BPS equation and show that all 1/4 BPS solutions are generated by an Nc x Nf matrix which is holomorphic in two complex variables, assuming the vector multiplet BPS equation does not give additional moduli. We determine the total moduli space formed by topological sectors patched together and work out the multi-instanton solution inside a single vortex with complete moduli. Small instanton singularities are interpreted as small sigma-model lump singularities inside the vortex. The relation between monopoles and instantons in the Higgs phase is also clarified as limits of calorons in the Higgs phase. Another type of instantons stuck at an intersection of two vortices and dyonic instantons in the Higgs phase are also discussed.

32 pages, 6 figures, typos corrected, comments and references added

References in corpus (67)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Small Instantons in String Theory
• Instantons on noncommutative R^4, and (2,0) superconformal six dimensional theory
• Vortices, Instantons and Branes
• Semilocal and Electroweak Strings
• Nonabelian Superconductors: Vortices and Confinement in $\mathcal{N}=2$ SQCD
• Periodic Instantons with non-trivial Holonomy
• Vortex Strings and Four-Dimensional Gauge Dynamics
• Non-Abelian String Junctions as Confined Monopoles
• Supertubes
• Monopole Constituents inside SU(n) Calorons
• Monopoles and Instantons on Partially Compactified D-Branes
• All Exact Solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield Equation
• Exact T-duality between Calorons and Taub-NUT spaces
• Monopoles in the Higgs Phase
• Construction of Non-Abelian Walls and Their Complete Moduli Space
• Non-Abelian Walls in Supersymmetric Gauge Theories
• Nonabelian Monopoles and the Vortices that Confine Them
• The Moduli Space of BPS Domain Walls
• Instantons on Noncommutative R^4 and Projection Operators
• Semilocal Topological Defects
• The BPS Spectra of Gauge Theories in Two and Four Dimensions
• Multi-Domain Walls in Massive Supersymmetric Sigma-Models
• Manifest Supersymmetry for BPS Walls in N=2 Nonlinear Sigma Models
• Branes within Branes
• Dyonic Instantons in Five Dimensional Gauge Theories
• Instantons and Magnetic Monopoles on $R^3\times S^1$ with Arbitrary Simple Gauge Groups
• Semilocal strings and monopoles
• Monopoles, Vortices, Domain Walls and D-Branes: The Rules of Interaction
• D-brane Construction for Non-Abelian Walls
• An Exact Solution of BPS Domain Wall Junction
• Mirror Mirror On The Wall: On 2d Black Holes and Liouville Theory
• Seiberg-Witten prepotential from instanton counting
• Semilocal Defects
• The BPS Spectra of Two-Dimensional Supersymmetric Gauge Theories with Twisted Mass Terms
• Global Structure of Moduli Space for BPS Walls
• BPS String Solutions in Non-Abelian Yang-Mills Theories and Confinement
• BPS Wall in N=2 SUSY Nonlinear Sigma Model with Eguchi-Hanson Manifold
• Nonnormalizable Zero Modes on BPS Junctions
• Vacua of Massive Hyper-Kahler Sigma Models with Non-Abelian Quotient
• Effective Theory on Non-Abelian Vortices in Six Dimensions
• Massive Nonlinear Sigma Models and BPS Domain Walls in Harmonic Superspace
• Domain Wall Junction in N=2 Supersymmetric QED in four dimensions
• BPS Walls and Junctions in SUSY Nonlinear Sigma Models
• A Note on 1/4-BPS States
• Color superconductivity, Z_N flux tubes and monopole confinement in deformed N=2* super Yang-Mills theories
• Monopoles Can be Confined by 0, 1 or 2 Vortices
• Z_k String fluxes and monopole confinement in non-Abelian theories
• Supertubes connecting D4 branes
• D-brane Configurations for Domain Walls and Their Webs
• Sigma-model soliton intersections from exceptional calibrations
• Geometry of the Nonabelian DBI Dyonic Instanton
• Dyonic Instanton as Supertube between D4 Branes
• The Heterotic Dyonic Instanton
• Symmetric Calorons
• An Exact Solution of BPS Junctions and Its Properties
• Field Theory Supertubes
• Walls and vortices in supersymmetric non-abelian gauge theories
• Non-BPS Walls and Their Stability in 5D Supersymmetric Theory
• Non-Abelian Walls and Vortices in Supersymmetric Theories
• BPS Domain Walls in Massive Hyper-Kahler Sigma Models
• 1/4 BPS Dyonic Calorons
• Domain Walls with Massive Hypermultiplets
• Color superconductivity, BPS strings and monopole confinement in N=2 and N=4 super Yang-Mills theories
• BPS Walls and Junctions in $\mathcal{N}=1$ SUSY Nonlinear Sigma Models

Cited by in corpus (129)

• Solitons in the Higgs phase -- the moduli matrix approach --
• Moduli Space of Non-Abelian Vortices
• TASI Lectures on Solitons
• Quantum Vortex Strings: A Review
• Non-Abelian Vortices of Higher Winding Numbers
• Vortices and Other Topological Solitons in Dense Quark Matter
• On the moduli space of semilocal strings and lumps
• Non-Abelian Vortices on Cylinder -- Duality between vortices and walls
• Manifestly Supersymmetric Effective Lagrangians on BPS Solitons
• Instabilities of Non-Abelian Vortices in Dense QCD
• Monopoles, Vortices, Domain Walls and D-Branes: The Rules of Interaction
• 1/2, 1/4 and 1/8 BPS Equations in SUSY Yang-Mills-Higgs Systems -- Field Theoretical Brane Configurations --
• Non-Abelian duality from vortex moduli: a dual model of color-confinement
• Color Magnetic Flux Tubes in Dense QCD. II: Effective World-Sheet Theory
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• D-brane Construction for Non-Abelian Walls
• Constructing Non-Abelian Vortices with Arbitrary Gauge Groups
• Josephson vortices and the Atiyah-Manton construction
• Webs of Walls
• Non-perturbative Contributions from Complexified Solutions in $\mathbb{C}{P}^{N-1}$ Models
• Correspondence between Skyrmions in 2+1 and 3+1 Dimensions
• Jewels on a wall ring
• Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
• Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
• Global Structure of Moduli Space for BPS Walls
• Incarnations of Skyrmions
• Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}{P}^{N-1}$ models
• Domain Walls with Non-Abelian Clouds
• Statistical Mechanics of Vortices from D-branes and T-duality
• BPS States in Supersymmetric Chiral Models with Higher Derivative Terms
• O(3) nonlinear sigma model in 1+1 dimensions with matrix product states
• Intersecting Solitons, Amoeba and Tropical Geometry
• Dual lattice representations for O(N) and CP(N-1) models with a chemical potential
• Non-Abelian Vortices in SO(N) and USp(N) Gauge Theories
• Fractional Vortices and Lumps
• Non-Abelian Sine-Gordon Solitons
• Dynamics of Domain Wall Networks
• Hyper-Kahler Sigma Models on (Co)tangent Bundles with SO(n) isometry
• Fractional instantons and bions in the O(N) model with twisted boundary conditions
• Confined Monopoles Induced by Quantum Effects in Dense QCD
• Non-Abelian Sine-Gordon Solitons: Correspondence between $SU(N)$ Skyrmions and $\mathbb{C}{P}^{N-1}$ Lumps
• Surface defects and instanton-vortex interaction
• Brane necklaces and brane coils
• Classifying BPS States in Supersymmetric Gauge Theories Coupled to Higher Derivative Chiral Models
• Vortices and Monopoles in Mass-deformed SO and USp Gauge Theories
• Topological order in a color-flavor locked phase of $(3+1)$-dimensional $U(N)$ gauge-Higgs system
• Studying Boojums in N=2 Theory with Walls and Vortices
• Relations among topological solitons
• Non-Abelian Monopoles in the Higgs Phase
• Non-BPS exact solutions and their relation to bions in $\mathbb{C}{P}^{N-1}$ models
• Effective Action of Domain Wall Networks
• Resurgence Structure to All Orders of Multi-bions in Deformed SUSY Quantum Mechanics
• Higher Derivative Corrections to Manifestly Supersymmetric Nonlinear Realizations
• SO and USp Kahler and Hyper-Kahler Quotients and Lumps
• Multiple Layer Structure of Non-Abelian Vortex
• Moduli Space of BPS Walls in Supersymmetric Gauge Theories
• Topological solitons in the supersymmetric Skyrme model
• Decomposing Instantons in Two Dimensions
• Dynamics of Strings between Walls
• Phase diagram of QCD matter with magnetic field: domain-wall Skyrmion chain in chiral soliton lattice
• Non-Abelian Global Vortices
• Static Interactions of non-Abelian Vortices
• Instantons in Chiral Magnets
• Fractional instanton of the SU($3$) gauge theory in weak coupling regime
• The Moduli Space Metric for Well-Separated Non-Abelian Vortices
• Phase structure of the twisted $SU(3)/U(1{)}^2$ flag sigma model on $\mathbb{R}\times S^1$
• Group Theory of Non-Abelian Vortices
• New BPS Objects in N=2 Supersymmetric Gauge Theories
• Josephson junction of non-Abelian superconductors and non-Abelian Josephson vortices
• Manifestations of magnetic vortices in equation of state of Yang-Mills plasma
• Neutral bions in the CP^{N-1} model for resurgence
• Winding Hopfions on R^2 x S^1
• Quantum toroidal algebras and solvable structures in gauge/string theory
• Dynamics of Non-Abelian Vortices
• Josephson instantons and Josephson monopoles in a non-Abelian Josephson junction
• Topological Nambu monopole in two Higgs doublet models
• Dyonic Instantons in 5-dim Yang-Mills Chern-Simons Theories
• Chiral Magnets from String Theory
• Nonlinear sigma models at nonzero chemical potential: breaking up instantons and the phase diagram
• Fractionalized Non-Self-Dual Solutions in the CP(N-1) Model
• Infrared renormalon in the supersymmetric $\mathbb{C}{P}^{N-1}$ model on $\mathbb{R}\times S^1$
• Revisiting the Faddeev-Skyrme Model and Hopf Solitons
• Confinement-Deconfinement Crossover in the Lattice $\mathbb{C}{P}^{N-1}$ Model
• 2d Partition Function in Omega-background and Vortex/Instanton Correspondence
• Instantons confined by monopole strings
• Defect formation from defect--anti-defect annihilations
• Fractional Skyrmion molecules in a $\mathbb{C}{P}^{N-1}$ model
• Topological Defects in the Georgi-Machacek Model
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Type I Non-Abelian Superconductors in Supersymmetric Gauge Theories
• Supertubes in Field Theories
• Non-Abelian Vortices without Dynamical Abelianization
• Incarnations of Instantons
• Walls of massive Kähler sigma models on SO(2N)/U(N) and Sp(N)/U(N)
• Chiral non-Abelian vortices and their confinement in three flavor dense QCD
• Solitons in Supersymmetric Gauge Theories: Moduli Matrix Approach
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• Solitons in Supersymmetric Gauge Theories
• Vacua and walls of mass-deformed Kähler nonlinear sigma models on $SO(2N)/U(N)$
• Non-integrability of Self-dual Yang-Mills-Higgs System
• Aharonov-Bohm defects
• Strongly coupled QFT dynamics via TQFT coupling
• Complex instantons in sigma models with chemical potential
• Exact solutions of domain wall junctions in arbitrary dimensions
• Non-Abelian Vortex-String Dynamics from Nonlinear Realization
• Knotted instantons from annihilations of monopole-instanton complex
• Solitonic ground state in supersymmetric theory in background
• Effective Action of Non-Abelian Monopole-Vortex Complex
• Winding theta and destructive interference of instantons
• J-kink domain walls and the DBI action
• Zero-modes of Non-Abelian Solitons in Three Dimensional Gauge Theories
• Vacuum energy of the supersymmetric $\mathbb{C}{P}^{N-1}$ model on $\mathbb{R}\times S^1$ in the $1/N$ expansion
• Partition Functions of $\mathcal{N}=1$ Gauge Theories on $S^2\times {\mathbb{R}}_{\epsilon }^2$ and Duality
• Higher Derivative Supersymmetric Nonlinear Sigma Models on Hermitian Symmetric Spaces, and BPS States Therein
• Walls in supersymmetric massive nonlinear sigma model on complex quadric surface
• BPS Boojums in N=2 supersymmetric gauge theories I
• Infrared renormalon in $SU(N)$ QCD(adj.) on ${\mathbb{R}}^3\times S^1$
• BPS pion domain walls in the supersymmetric chiral Lagrangian
• Sigma Model BPS Lumps on Torus
• Gauge symmetry breaking in ten-dimensional Yang-Mills theory dynamically compactified on S^6
• Dual formulations of vortex strings in supersymmetric Abelian Higgs model
• Confinement and moduli locking of Alice strings and monopoles
• BPS Boojums in N=2 supersymmetric gauge theories II
• Trions in 1+1 dimensions
• Massive Nambu-Goldstone Fermions and Bosons for Non-relativistic Superconformal Symmetry: Jackiw-Pi Vortices in a Trap
• On the ADHM construction of noncommutative U(2) k-instanton
• Holographic QCD Matter: Chiral Soliton Lattices in Strong Magnetic Field
• Chiral non-Abelian vortex molecules in dense QCD
• Colliding Waves on a Brane, the Big Bounce and Reconnection