TASI Lectures on Solitons

Abstract

These lectures cover aspects of solitons with focus on applications to the quantum dynamics of supersymmetric gauge theories and string theory. The lectures consist of four sections, each dealing with a different soliton. We start with instantons and work down in co-dimension to monopoles, vortices and, eventually, domain walls. Emphasis is placed on the moduli space of solitons and, in particular, on the web of connections that links solitons of different types. The D-brane realization of the ADHM and Nahm construction for instantons and monopoles is reviewed, together with related constructions for vortices and domain walls. Each lecture ends with a series of vignettes detailing the roles solitons play in the quantum dynamics of supersymmetric gauge theories in various dimensions. This includes applications to the AdS/CFT correspondence, little string theory, S-duality, cosmic strings, and the quantitative correspondence between 2d sigma models and 4d gauge theories.

139 (small) pages. Lots of figures. This is an extended write up of lectures given at TASI, June 2005. v2-5: typos corrected, references added

References in corpus (124)

• Large N Field Theories, String Theory and Gravity
• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Phases of $N=2$ Theories In Two Dimensions
• Cosmic strings
• Solutions Of Four-Dimensional Field Theories Via M Theory
• Supergravity and The Large N Limit of Theories With Sixteen Supercharges
• Mirror Symmetry in Three Dimensional Gauge Theories
• The D1/D5 System And Singular CFT
• TASI Lectures on D-Branes
• Born-Infeld particles and Dirichlet p-branes
• Duality, Quotients, and Currents
• Brane Dynamics and Gauge Theory
• Semilocal and Electroweak Strings
• On Classification of N=2 Supersymmetric Theories, (e-mail uncorrupted version)
• Dyon - Monopole Bound States, Self-Dual Harmonic Forms on the Multi-Monopole Moduli Space, and SL(2,Z) Invariance in String Theory
• Nonabelian Superconductors: Vortices and Confinement in $\mathcal{N}=2$ SQCD
• Holography and Defect Conformal Field Theories
• The Condensed Matter Physics of QCD
• Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties
• Vortex Strings and Four-Dimensional Gauge Dynamics
• Non-Abelian String Junctions as Confined Monopoles
• On Mirror Symmetry in Three Dimensional Abelian Gauge Theories
• A Matrix Model for the Two Dimensional Black Hole
• Gauge Fields and D-branes
• Mirror Symmetry in Three-Dimensional Gauge Theories, Quivers and D-branes
• Duality of the Fermionic 2d Black Hole and N=2 Liouville Theory as Mirror Symmetry
• A brief review of "little string theories"
• Matrix Description of M-theory on $T^4$ and $T^5$
• QCD and dimensional deconstruction
• Gauge Dynamics And Compactification To Three Dimensions
• Mirror Symmetry in Three-Dimensional Gauge Theories, SL(2,Z) and D-Brane Moduli Spaces
• NS5-Branes, T-Duality and Worldsheet Instantons
• Lectures on D-branes
• Branes and N=2 Theories in Two Dimensions
• Monopoles and Instantons on Partially Compactified D-Branes
• Non-perturbative Effects in AdS5 * S5 String Theory and d=4 SUSY Yang-Mills
• INSTANTON CALCULATIONS VERSUS EXACT RESULTS IN 4 DIMENSIONAL SUSY GAUGE THEORIES.
• D-Brane Primer
• All Exact Solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield Equation
• Instantons in supersymmetric Yang-Mills and D-instantons in IIB superstring theory
• Monopoles in the Higgs Phase
• Multi-Instanton Calculus in $N=2$ Supersymmetric Gauge Theory
• Instantons in the Higgs Phase
• Multi-Instanton Calculus and the AdS/CFT Correspondence in N=4 Superconformal Field Theory
• Three-Dimensional Gauge Dynamics from Brane Configurations with (p,q)-Fivebrane
• Komaba Lectures on Noncommutative Solitons and D-Branes
• Three-Pronged Strings and 1/4 BPS States in N=4 Super-Yang-Mills Theory
• Branes and Mirror Symmetry in N=2 Supersymmetric Gauge Theories in Three Dimensions
• Construction of Non-Abelian Walls and Their Complete Moduli Space
• The Moduli Space Metric for Well Separated BPS Monoples
• Non-Abelian Walls in Supersymmetric Gauge Theories
• Nonabelian Monopoles and the Vortices that Confine Them
• The Moduli Space of BPS Domain Walls
• D-brane Solitons in Supersymmetric Sigma-Models
• Localization of Non-Abelian Gauge Fields on Domain Walls at Weak Coupling (D-brane Prototypes)
• The Moduli Space of Many BPS Monopoles for Arbitrary Gauge Groups
• Asymptotic Interactions of Critically Coupled Vortices
• Three Dimensional Gauge Theories and Monopoles
• BPS Monopoles
• Manifest Supersymmetry for BPS Walls in N=2 Nonlinear Sigma Models
• Dyons in N=4 Supersymmetric Theories and Three-Pronged Strings
• Multi-Domain Walls in Massive Supersymmetric Sigma-Models
• Branes within Branes
• Domain Walls and Flux Tubes in N=2 SQCD: D-Brane Prototypes
• Worldsheet Instanton Corrections to the Kaluza-Klein Monopole
• Trieste lectures on solitons in noncommutative gauge theories
• Nielsen-Olesen Vortices in Noncommutative Abelian Higgs Model
• Monopoles, Vortices, Domain Walls and D-Branes: The Rules of Interaction
• Reconnection of Non-Abelian Cosmic Strings
• Solitonic D-branes and brane annihilation
• Noncommutative Vortex Solitons
• 1/2, 1/4 and 1/8 BPS Equations in SUSY Yang-Mills-Higgs Systems -- Field Theoretical Brane Configurations --
• Strong Coupling Dynamics of Branes from M-theory
• D-brane Construction for Non-Abelian Walls
• Skyrmions from Instantons inside Domain Walls
• Mirror Mirror On The Wall: On 2d Black Holes and Liouville Theory
• Membrane Scattering with M-Momentum Transfer
• Webs of Walls
• Dynamics of N=2 Supersymmetric Chern-Simons Theories
• Mirror Symmetry and Toric Geometry in Three-Dimensional Gauge Theories
• Non-Abelian Vortices in N=1* Gauge Theory
• Non-Abelian Webs of Walls
• D3-branes on the Coulomb branch and instantons
• Nahm's equations, $N=1^{\ast }$ domain walls, and D-strings in $Ad{S}_{5}x{S}_5$
• Global Structure of Moduli Space for BPS Walls
• Supersymmetric Quantum Mechanics of Monopoles in N=4 Yang-Mills Theory
• Low Energy Dynamics for 1/4 BPS Dyons
• Nonvanishing quantum corrections to the mass and central charge of the N=2 vortex and BPS saturation
• Exact Wall Solutions in 5-Dimensional SUSY QED at Finite Coupling
• Multi-Instantons, Three-Dimensional Gauge Theory, and the Gauss-Bonnet-Chern Theorem
• BPS Wall in N=2 SUSY Nonlinear Sigma Model with Eguchi-Hanson Manifold
• Monopoles in String Theory
• Dirichlet Topological Defects
• Massive Nonlinear Sigma Models and BPS Domain Walls in Harmonic Superspace
• Dynamics of Multiple Kaluza-Klein Monopoles in M- and String Theory
• Domain Wall Junction in N=2 Supersymmetric QED in four dimensions
• The anomaly in the central charge of the supersymmetric kink from dimensional regularization and reduction
• A Classical Manifestation of the Pauli Exclusion Principle
• Quantum Spectrum of Instanton Solitons in Five Dimensional Noncommutative U(N) Theories
• The moduli space of two U(1) instantons on noncommutative $R^4$ and $R^3\times S^1$
• General Low Energy Dynamics of Supersymmetric Monopoles
• An Index Theorem for Domain Walls in Supersymmetric Gauge Theories
• Studying Boojums in N=2 Theory with Walls and Vortices
• Domain Walls and Flux Tubes
• Z_k String fluxes and monopole confinement in non-Abelian theories
• Motion on moduli spaces with potentials
• Moduli Space of BPS Walls in Supersymmetric Gauge Theories
• Dimensional Deconstruction and Wess-Zumino-Witten Terms
• Instantons in $\mathcal{N}=2$ $Sp(N)$ Superconformal Gauge Theories and the AdS/CFT Correspondence
• Supersymmetry and the Multi-Instanton Measure
• A new anomalous contribution to the central charge of the N=2 monopole
• Topological Solitons from DeConstructed Extra Dimensions
• A note on the (1, 1,..., 1) monopole metric
• Stringy Derivation of Nahm Construction of Monopoles
• N=2 Sigma Model with Twisted Mass and Superpotential: Central Charges and Solitons
• Explicit Multimonopole Solutions in SU(N) Gauge Theory
• Maxwell Chern-Simons Solitons from Type IIB String Theory
• New BPS Objects in N=2 Supersymmetric Gauge Theories
• ADHM and D-instantons in orbifold AdS/CFT duality
• ADHMN boundary conditions from removing monopoles
• Notes on Soliton Bound-State Problems in Gauge Theory and String Theory
• Summing the Instanton Series in N=2 Superconformal Large-N QCD
• Instantons, finite N=2 Sp(N) theories and the AdS/CFT correspondence
• Non-Abelian Walls and Vortices in Supersymmetric Theories

Cited by in corpus (115)

• Physics of Strongly coupled Quark-Gluon Plasma
• Solitons in the Higgs phase -- the moduli matrix approach --
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Non-Abelian Semilocal Strings in N=2 Supersymmetric QCD
• On the moduli space of semilocal strings and lumps
• Non-Abelian Vortices on Cylinder -- Duality between vortices and walls
• Color Magnetic Flux Tubes in Dense QCD
• Heterotic Vortex Strings
• Non-Abelian duality from vortex moduli: a dual model of color-confinement
• Color Magnetic Flux Tubes in Dense QCD. II: Effective World-Sheet Theory
• Constructing Non-Abelian Vortices with Arbitrary Gauge Groups
• Integrability of Vortex Equations on Riemann Surfaces
• Heterotic Flux Tubes in N=2 SQCD with N=1 Preserving Deformations
• (2,0) Supersymmetry and the Light-Cone Description of M5-branes
• Domain Walls with Non-Abelian Clouds
• Five-Brane Superpotentials and Heterotic/F-theory Duality
• Large-N Solution of the Heterotic N=(0,2) Two-Dimensional CP(N-1) Model
• Intersecting Solitons, Amoeba and Tropical Geometry
• Effective World-Sheet Theory for Non-Abelian Semilocal Strings in N = 2 Supersymmetric QCD
• Noncommutative Ward's Conjecture and Integrable Systems
• Holographic flavor on the Higgs branch
• Parameter counting for singular monopoles on R^3
• Fractional Vortices and Lumps
• Hyper-Kahler Sigma Models on (Co)tangent Bundles with SO(n) isometry
• Dynamics of Domain Wall Networks
• Multi-monopoles and Magnetic Bags
• Magnetic strings in Lattice QCD as Nonabelian Vortices
• Non-Abelian Confinement in N=2 Supersymmetric QCD: Duality and Kinks on Confining Strings
• Topological order in a color-flavor locked phase of $(3+1)$-dimensional $U(N)$ gauge-Higgs system
• Confined Magnetic Monopoles in Dense QCD
• Non-Abelian Duality and Confinement in N=2 Supersymmetric QCD
• Non-Abelian Chern-Simons vortices with generic gauge groups
• SO and USp Kahler and Hyper-Kahler Quotients and Lumps
• Multiple Layer Structure of Non-Abelian Vortex
• Non-Abelian Vortex in Four Dimensions as a Critical String on a Conifold
• Decomposing Instantons in Two Dimensions
• Spontaneous Magnetization through Non-Abelian Vortex Formation in Rotating Dense Quark Matter
• The Geometric Phase in Supersymmetric Quantum Mechanics
• Dynamics of Strings between Walls
• The Dynamics of Chern-Simons Vortices
• Fractional and semi-local non-Abelian Chern-Simons vortices
• Superconformal Vortex Strings
• Matrix Models and D-branes in Twistor String Theory
• Coexisting Vortices and Antivortices Generated by Dually Gauged Harmonic Maps
• The Moduli Space Metric for Well-Separated Non-Abelian Vortices
• Critical Non-Abelian Vortex in Four Dimensions and Little String Theory
• Domain Lines as Fractional Strings
• Non-Abelian k-Vortex Dynamics in N=1^* theory and its Gravity Dual
• Aharonov-Bohm Phase in High Density Quark Matter
• Non-Abelian String of a Finite Length
• Dynamics of Non-Abelian Vortices
• Quantum Mass and Central Charge of Supersymmetric Monopoles - Anomalies, current renormalization, and surface terms
• Dyonic Instantons in 5-dim Yang-Mills Chern-Simons Theories
• Monopoles and Wilson Lines
• On the Stability of Non-Abelian Semi-local Vortices
• Hadrons of N=2 Supersymmetric QCD in Four Dimensions from Little String Theory
• Non-Abelian Duality and Confinement: from N=2 to N=1 Supersymmetric QCD
• Instantons, Twistors, and Emergent Gravity
• Description of the Heterotic String Solutions in U(N) SQCD
• 2d Partition Function in Omega-background and Vortex/Instanton Correspondence
• r Duality and "Instead-of-Confinement" Mechanism in N=1 Supersymmetric QCD
• The non-Abelian tensor multiplet in loop space
• Strong versus Weak Coupling Confinement in N=2 Supersymmetric QCD
• Non-Abelian Vortices without Dynamical Abelianization
• Moduli Space Potentials for Heterotic non-Abelian Flux Tubes: Weak Deformation
• String "Baryon'' in Four-Dimensional $\mathcal{N}=2$ Supersymmetric QCD from 2D-4D Correspondence
• Crossover between Abelian and non-Abelian confinement in N=2 supersymmetric QCD
• Non-Abelian Vortices on the Torus
• Nonabelian strings in a dense matter
• Heterotic N=(0,2) CP(N-1) Model with Twisted Masses
• Soliton Junctions in the Large Magnetic Flux Limit
• D-branes and Azumaya/matrix noncommutative differential geometry, I: D-branes as fundamental objects in string theory and differentiable maps from Azumaya/matrix manifolds with a fundamental module to real manifolds
• Non-integrability of Self-dual Yang-Mills-Higgs System
• Non-Abelian strings in N=1 supersymmetric QCD
• Confinement and Localization on Domain Walls
• Confronting Seiberg's Duality with r Duality in N=1 Supersymmetric QCD
• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• Low Energy Dynamics of Monopoles in Supersymmetric Yang-Mills Theories with Hypermultiplets
• Hybrid r-Vacua in N=2 Supersymmetric QCD: Universal Condensate Formula
• Five-dimensional super Yang-Mills theory from ABJM theory
• Brane Realization of Nambu Monopoles and Electroweak Strings
• Non-Abelian Vortex-String Dynamics from Nonlinear Realization
• Symmetry Operators and Gravity
• Persistent Challenges of Quantum Chromodynamics
• Composite Non-Abelian Strings with Grassmannian Models on the World Sheet
• Flux Compactification for the Critical Non-Abelian Vortex and Quark Masses
• Four-dimensional SYM probes in wrapped M5-brane backgrounds
• Effective Action of Non-Abelian Monopole-Vortex Complex
• Vortex counting and the quantum Hall effect
• J-kink domain walls and the DBI action
• Quantum Deformation of the Effective Theory on Non-Abelian string and 2D-4D correspondence
• Description of the Heterotic String Solutions in the M Model
• On The Problem of the Quantum Heterotic Vortex
• Heterotic Non-Abelian String of a Finite Length
• 2D-4D Correspondence: Towers of Kinks versus Towers of Monopoles in N=2 Theories
• Non Abelian Vortices as Instantons on Noncommutative Discrete Space
• Cosmic Strings with Small Tension
• Vortices as Instantons in Noncommutative Discrete Space: Use of $Z_2$ Coordinates
• Connecting Localization and Wall-Crossing via D-Branes
• Non-Abelian vortex in lattice gauge theory
• Static Interactions of U(N) non-Abelian Vortices
• Non-Abelian Strings: From Weak to Strong Coupling and Back via Duality
• Central charges of wrapped M5-brane backgrounds
• Dual formulations of vortex strings in supersymmetric Abelian Higgs model
• Vortices which do not Abelianize dynamically: Semi-classical origin of non-Abelian monopoles
• Applications of String Theory: Non-perturbative Effects in Flux Compactifications and Effective Description of Statistical Systems
• Comments on the N=1 SU(M+p)xSU(p) quiver gauge theory with flavor
• Les Houches lectures on non-perturbative Seiberg-Witten geometry
• Effective Lagrangian of Domain Wall Networks
• Dynamics of non-Abelian strings in supersymmetric gauge theories
• Domain Walls, The Extended Superconformal Algebra, and The Supercurrent
• Index Theorem for non-Supersymmetric Fermions Coupled to a non-Abelian String and Electric Charge Quantization
• Solitons on Singularities
• Moduli Space Dynamics of Noncommutative U(2) Instantons