Komaba Lectures on Noncommutative Solitons and D-Branes

Abstract

These lectures provide an introduction to noncommutative geometry and its origins in quantum mechanics and to the construction of solitons in noncommutative field theory. These ideas are applied to the construction of D-branes as solitons of the tachyon field in noncommutative open string theory. A brief discussion is given of the K-theory classification of D-brane charge in terms of the K-theory of operator algebras. Based on lectures presented at the Komaba 2000 workshop, Nov. 14-16 2000.

43 pages, harvmac (b)

Cited by in corpus (99)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Introduction to M(atrix) theory and noncommutative geometry
• Introduction to M(atrix) theory and noncommutative geometry, Part II
• TASI Lectures on Solitons
• Noncommutative Field Theories and Gravity
• Split string field theory I
• Coherent State Induced Star-Product on $R_{\lambda }^3$ and the Fuzzy Sphere
• Non-Abelian Vortices on Cylinder -- Duality between vortices and walls
• An Exact Solution to Seiberg-Witten Equation of Noncommutative Gauge Theory
• Towards Noncommutative Integrable Systems
• The Meaning of Infrared Singularities in Noncommutative Gauge Theories
• Brane-Antibrane Systems at Finite Temperature and the Entropy of Black Branes
• The singular geometry of the sliver
• Open string field theory without open strings
• Line operators on S^1xR^3 and quantization of the Hitchin moduli space
• Soliton-Antisoliton Scattering Configurations in a Noncommutative Sigma Model in 2+1 Dimensions
• Instability of Non-Commutative SYM Theories at Finite Temperature
• Exact Noncommutative KP and KdV Multi-solitons
• Absence of Higher Order Corrections to Noncommutative Chern-Simons Coupling
• Noncommutative Solitons and D-branes
• Rank Two Quiver Gauge Theory, Graded Connections and Noncommutative Vortices
• Topics in String Field Theory
• A Note on Noncommutative Chern-Simons Theories
• Noncommutative Extended Waves and Soliton-like Configurations in N=2 String Theory
• Noncommutative o*(N) and usp*(2N) algebras and the corresponding gauge field theories
• Noncommutative Ward's Conjecture and Integrable Systems
• ADHM/Nahm Construction of Localized Solitons in Noncommutative Gauge Theories
• Noncommutative Instantons in Higher Dimensions, Vortices and Topological K-Cycles
• Gauge Invariance and Tachyon Condensation in Open String Field Theory
• Chiral Anomaly on Fuzzy 2-Sphere
• Exact solitons on noncommutative tori
• Vacuum String Field Theory with B field
• Sigma-Model Solitons in the Noncommutative Plane: Construction and Stability Analysis
• On Reductions of Noncommutative Anti-Self-Dual Yang-Mills Equations
• Gauge Theories on Deformed Spaces
• Supersymmetric quantum mechanics on noncommutative space
• The Existence and Stability of Noncommutative Scalar Solitons
• Interaction of Noncommutative Plane Waves in 2+1 Dimensions
• Towards Noncommutative Integrable Equations
• Seiberg-Witten Monopole Equations on Noncommutative R^4
• Exact noncommutative solitons in p-adic strings and BSFT
• Branes and instantons intersecting at angles
• The Decay of Unstable Noncommutative Solitons
• D1-Strings in Large RR 3-Form Flux, Quantum Nambu Geometry and M5-Branes in C-Field
• Moduli-Space Dynamics of Noncommutative Abelian Sigma-Model Solitons
• Fractional quantum Hall effect on the two-sphere: a matrix model proposal
• D-branes as GMS Solitons in Vacuum String Field Theory
• Noncommutative solitons on Kahler manifolds
• Noncommutative Vortices and Flux-Tubes from Yang-Mills Theories with Spontaneously Generated Fuzzy Extra Dimensions
• The Moduli Space of Noncommutative Vortices
• Nambu-Goto Strings from SU(N) Born-Infeld model
• Scalar Solitons in Non(anti)commutative Superspace
• Anomalies in Noncommutative Dipole Field Theories
• Noncommutative Integrable Systems and Quasideterminants
• Gauge Fields on Tori and T-duality
• Instantons on General Noncommutative R^4
• Lost equivalence of nonlinear sigma and $C{P}^1$ models on noncommutative space
• Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
• Bubbling AdS and Vacuum String Field Theory
• Noncommutative Maxwell-Chern-Simons theory (I): One-loop dispersion relation analysis
• Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED
• Topology of the Gauge Group in Noncommutative Gauge Theory
• The QCD Membrane
• Reverse Engineering ADHM Construction from Non-Commutative Instantons
• Transmogrifying Fuzzy Vortices
• Scalar Solitons on the Fuzzy Sphere
• Noncommutative Solitons of Gravity
• Non BPS noncommutative vortices
• Analytical and numerical analysis of a rotational invariant D=2 harmonic oscillator in the light of different noncommutative phase-space configurations
• Noncommutative Fluids
• D0 Matrix Mechanics: New Fuzzy Solutions at Large N
• Gauge Invariance and Noncommutativity
• Noncommutative geometry and fundamental interactions: the first ten years
• Elliptic Algebra and Integrable Models for Solitons on Noncummutative Torus $\mathcal{T}$
• Soliton Solutions on Noncommutative Orbifold $ T^2/Z_4
• Domain walls in noncommutative gauge theories, folded D-branes, and communication with mirror world
• Blocking up D-branes : Matrix renormalization ?
• Matrix Effective Theories of the Fractional Quantum Hall effect
• Angles in Fuzzy Disc and Angular Noncommutative Solitons
• p-p' System with B Field and Projection Operator Noncommutative Solitons
• Noncommutative Baby Skyrmions
• Interpolating State in String Field Theory
• Noncommutativity and Duality through the Symplectic Embedding Formalism
• Vortices as Instantons in Noncommutative Discrete Space: Use of $Z_2$ Coordinates
• Solitons of Sigma Model on Noncommutative Space as Solitons of Electron System
• Some Notes Concerning the Dynamics of Noncommutative Lumps Corresponding to Nontrivial Vacua in Noncommutative Yang--Mills Models which are perturbative branches of M(atrix) Theory
• Puffed Noncommutative Nonabelian Vortices
• Noncommutative Nonlinear Sigma Models and Integrability
• Exact BPS bound for noncommutative baby Skyrmions
• ADHM Construction of Noncommutative Instantons
• Remarks on Noncommutative Solitons
• Noncommutative Solitons and the W_{1+\infty} Algebras in Quantum Hall Theory
• D-Branes in Noncommutative Field Theory
• Gauge theory solitons on noncommutative cylinder
• Quantization of Noncommutative Scalar Solitons at finite $\theta$
• On the Moduli Space of Noncommutative Multi-solitons at Finite Theta
• Noncommutative Q-Lumps
• D-branes, actions effectives et symétrie miroir