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Physics - Particle and Nuclear Physics | Strings, Conformal Fields, and Topology - An Introduction

Strings, Conformal Fields, and Topology

An Introduction

Kaku, Michio

Softcover reprint of the original 1st ed. 1991, XIV, 535 pp. 40 figs. in 50 parts

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Following on the foundations laid in his earlier book "Introduction to Superstrings", Professor Kaku discusses such topics as the classification of conformal string theories, the non-polynomial closed string field theory, matrix models, and topological field theory. The presentation of the material is self-contained, and several chapters review material expounded in the earlier book. This book provides students with an understanding of the main areas of current progress in string theory, placing the reader at the forefront of current research.

Content Level » Graduate

Related subjects » Particle and Nuclear Physics - Theoretical, Mathematical & Computational Physics

Table of contents 

I Conformal Field Theory and Perturbation Theory.- 1 Introduction to Superstrings.- 1.1. Introduction.- 1.2. Quantizing the Relativistic String.- 1.3. Scattering Amplitudes.- 1.4. Supersymmetry.- 1.5. 2D SUSY versus 10D SUSY.- 1.6. Types of Strings.- 1.7. 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 Correlation Functions.- 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.- 5 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 Towards 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 Beyond the Planck Length.- 9.1. Need for a Nonperturbative Approach.- 9.2. Duality at the Planck Scale.- 9.3. Possible Phase Transition at the Hagedorn Temperature.- 9.4. New Symmetries at High Energy.- 9.5. Is String Theory Borel Summable?.- 9.6. Nonperturbative Approaches.- 9.7. Renormalization Group Approach.- 9.8. Summary.- 10 String Field Theory.- 10.1. First Versus Second Quantization.- 10.2. Light Cone String Field Theory.- 10.3. Free BRST Action.- 10.4. Interacting BRST String Field Theory.- 10.5. Four-Point Amplitude.- 10.6. Superstring Field Theory.- 10.7. Picture Changing.- 10.8. Superstring Action.- 10.9. Summary.- 11 Nonpolynomial String Field Theory.- 11.1. Four-String Interaction.- 11.2. N-Sided Polyhedra.- 11.3. Nonpolynomial Action.- 11.4. Conformal Maps.- 11.5. Tadpoles.- 11.6. Summary.- 12 Geometrie String Field Theory.- 12.1. Why So Many String Field Theories?.- 12.2. The String Group.- 12.3. Universal String Group.- 12.4. How Long Is a String?.- 12.5. Cohomology.- 12.6. Interactions.- 12.7. From Polynomial to Nonpolynomial String Theory.- 12.8. Method of Reflections.- 12.9. Summary.- 13 2D Gravity and Matrix Models.- 13.1. Exactly Solvable Strings.- 13.2. 2D Gravity and KPZ.- 13.3. Matrix Models.- 13.4. Recursion Relations.- 13.5. KdV Hierarchy.- 13.6. Multimatrix Models.- 13.7. D=1 Matrix Models.- 13.8. Summary.- 14 Topological Field Theory.- 14.1. Unbroken Phase of String Theory.- 14.2. Topology and Morse Theory.- 14.3. Sigma Models and Floer Theory.- 14.4. Cohomological Topological Field Theories.- 14.5. Correlation Functions.- 14.6. Topological Sigma Models.- 14.7. Topological 2D Gravity.- 14.8. Correlation Functions for 2D Topological Gravity.- 14.9. Virasoro Constraint, W-algebras, and KP Hierarchies.- 14.10. Summary.- 14.11. Conclusion.- Appendix 1: Batalin-Vilkovisky Quantization.- Appendix 2: Covariant Quantization of the Green-Schwarz String.

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