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Physics - Quantum Physics | Strings, Conformal Fields, and M-Theory

Strings, Conformal Fields, and M-Theory

Kaku, Michio

2nd ed. 2000, XV, 531 p.

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String theory continues to progress at an astonishing rate, and this book brings the reader up to date with the latest developments and the most active areas of research in the field. Building on the foundations laid in his Introduction to Superstrings and M Theory, Professor Kaku discusses such topics as the classification of conformal string theories, knot theory, the Yang-Baxter relation, quantum groups, and the insights into 11-dimensional strings recently obtained from M-theory. New chapters discuss such topics as Seiberg- Witten theory, M theory and duality., and D-branes. Several chapters review the fundamentals of string theory, making the presentation of the material self-contained while keeping overlap with the earlier book to a minimum. This book conveys the vitality of the current research and places readers at its forefront.

Content Level » Graduate

Related subjects » Applied & Technical Physics - Quantum Physics

Table of contents 

I 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 Superstring Theories.- 14.3 T Duality.- 14.4 S duality.- 14.4.1 Type IIA and M-Theory.- 14.4.2 Type IIB.- 14.4.3 Type I Strings.- 14.5 BPS States.- 14.6 Supersymmetry and p-Branes.- 14.7 Compactification.- 14.8 Example: D = 6.- 14.8.1 D = 6, N = (2, 2) Theory.- 14.8.2 D = 6, N = (1, 1) Theories.- 14.8.3 Deletions and Fibrations.- 14.9 F-Theory.- 14.10 Summary.- 15 D-Branes and CFT/ADS Duality.- 15.1 Solitons.- 15.2 Supermembrane Action.- 15.3 5-Branes and D-Branes.- 15.4 D-Brane Actions.- 15.5 M(atrix)-Theory and Membranes.- 15.6 Black Holes.- 15.7 CFT/ADS Duality.- 15.8 Anti-de Sitter Space.- 15.9 AdS and QCD.- 15.10 Summary.- 15.11 Conclusion.

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