Including a review of the fundamentals of string theory, this book conveys the vitality of the research and provides an understanding of the research in the field. It contains chapters that discuss such topics as Seiberg-Witten theory, M theory and duality, and D-branes.

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InhaltsangabeI Conformal Field Theory and Perturbation Theory.- 1 Introduction to Superstrings.- 1.1 Quantizing the Relativistic String.- 1.2 Scattering Amplitudes.- 1.3 Supersymmetry.- 1.4 2D SUSY Versus 10D SUSY.- 1.5 Types of Strings.- 1.6 Summary.- 2 BPZ Bootstrap and Minimal Models.- 2.1 Conformal Symmetry in D Dimensions.- 2.2 Conformal Group in Two Dimensions.- 2.3 Representations of the Conformal Group.- 2.4 Fusion Rules and Correlations Function.- 2.5 Minimal Models.- 2.6 Fusion Rules for Minimal Models.- 2.7 Superconformal Minimal Series.- 2.8 Summary.- 3 WZW Model, Cosets, and Rational Conformal Field Theory.- 3.1 Compactification and the WZW Model.- 3.2 Frenkel-Kac Construction.- 3.3 GKO Coset Construction.- 3.4 Conformal and Current Blocks.- 3.5 Racah Coefficients for Rational Conformal Field Theory.- 3.6 Summary.- 4 Modular Invariance and the A-D-E Classification.- 4.1 Dehn Twists.- 4.2 Free Fermion and Boson Characters.- 4.3 GSO and Supersymmetry.- 4.4 Minimal Model Characters.- 4.5 Affine Characters.- 4.6 A-D-E Classification.- 4.7 Higher Invariants and Simple Currents.- 4.8 Diagonalizing the Fusion Rules.- 4.9 RCFT: Finite Number of Primary Fields.- 4.10 Summary.- N = 2 SUSY and Parafermions.- 5.1 Calabi-Yau Manifolds.- 5.2 N = 2 Superconformal Symmetry.- 5.3 N = 2 Minimal Series.- 5.4 N = 2 Minimal Models and Calabi-Yau Manifolds.- 5.5 Parafermions.- 5.6 Supersymmetric Coset Construction.- 5.7 Hermitian Spaces.- 5.8 Summary.- 6 Yang-Baxter Relation.- 6.1 Statistical Mechanics and Critical Exponents.- 6.2 One-Dimensional Ising Model.- 6.3 Two-Dimensional Ising Model.- 6.4 RSOS and Other Models.- 6.5 Yang-Baxter Relation.- 6.6 Solitons and the Yang-Baxter Equation.- 6.7 Summary.- 7 Toward a Classification of Conformal Field Theories.- 7.1 Feigin-Fuchs Free Fields.- 7.2 Free Field Realizations of Coset Theories.- 7.3 Landau-Ginzburg Potentials.- 7.4 N = 2 Chiral Rings.- 7.5 N = 2 Landau-Ginzburg and Catastrophe Theory.- 7.6 Zamolodchikov's c Theorem.- 7.7 A-D-E Classification of c = 1 Theories.- 7.8 Summary.- 8 Knot Theory and Quantum Groups.- 8.1 Chern-Simons Approach to Conformal Field Theory.- 8.2 Elementary Knot Theory.- 8.3 Jones Polynomial and the Braid Group.- 8.4 Quantum Field Theory and Knot Invariants.- 8.5 Knots and Conformal Field Theory.- 8.6 New Knot Invariants from Physics.- 8.7 Knots and Quantum Groups.- 8.8 Hecke and Temperley-Lieb Algebras.- 8.9 Summary.- II Nonperturbative Methods.- 9 String Field Theory.- 9.1 First Versus Second Quantization.- 9.2 Light Cone String Field Theory.- 9.3 Free BRST Action.- 9.4 Interacting BRST String Field Theory.- 9.5 Four-Point Amplitude.- 9.6 Superstring Field Theory.- 9.7 Picture Changing.- 9.8 Superstring Action.- 9.9 Summary.- 10 Non polynomial String Field Theory.- 10.1 Four-String Interaction.- 10.2 N-Sided Polyhedra.- 10.3 Nonpolynomial Action.- 10.4 Conformal Maps.- 10.5 Tadpoles.- 10.6 Summary.- 11 2D Gravity and Matrix Models.- 11.1 Exactly Solvable Strings.- 11.2 2D Gravity and KPZ.- 11.3 Matrix Models.- 11.4 Recursion Relations.- 11.5 KdV Hierarchy.- 11.6 Multimatrix Models.- 11.7 D = 1 Matrix Models.- 11.8 Summary.- 12 Topological Field Theory.- 12.1 Unbroken Phase of String Theory.- 12.2 Topology and Morse Theory.- 12.3 Sigma Models and Floer Theory.- 12.4 Cohomological Topological Field Theories.- 12.5 Correlation Functions.- 12.6 Topological Sigma Models.- 12.7 Topological 2D Gravity.- 12.8 Correlation Functions for 2D Topological Gravity.- 12.9 Virasoro Constraint, W-Algebras, and KP Hierarchies.- 12.10 Summary.- 13 Seiberg-Witten Theory.- 13.1 Introduction.- 13.2 Electric-Magnetic Duality.- 13.3 Holomorphic Potentials.- 13.4 N = 1 SUSY QCD.- 13.4.1 Nf < Nc.- 13.4.2 Nf = Nc.- 13.4.3 Nf = Nc + 1.- 13.4.4 Nc + 2 ? Nf ? 3/2Nc.- 13.4.5 3/2Nc < Nf < 3Nc.- 13.4.6 N ? 3Nc.- 13.4.7 SO(Nc) SUSY Gauge Theory.- 13.5 N = 2 SUSY Gauge Theory.- 13.6 SU(N)N = 2 SUSY Gauge Theory.- 13.7 Summary.- 14 M-Theory and Duality.- 14.1 Introduction.- 14.2 Unifying the Five Superstr

I. Conformal Fields and Perturbation Theory: Introduction to Superstrings. BPZ Bootstrap and Minimal Models. WZW Model, Cosets, and Rational Conformal Field Theory. Modular Invariance and The A-D-E Classification. N=2 SUSY and Parafermions.- Yang-Baxter Relation. Towards A Classification of Conformal Field Theories. Knot Theory and Quantum Groups.- II. Nonperturbative Methods: String Field Theories. Nonpolynomial String Field Theory. 2D Gravity and Matrix Models. Topological Field Theory. Seiberg-Witten Theory. M Theory and Duality. D-Branes and CFT /ADS Duality.