超弦和M理论导论 : 第2版

Preface

Acknowledgments

Ⅰ First Quantization and Path Integrals

1 Path Integrals and Point Particles

1.1 Why Strings?

1.2 Historical Review of Gauge Theory

1.3 Path Integrals and Point Particles

1.4 Relativistic Point Particles

1.5 First and Second Quantization

1.6 Faddeev-Popov Quantization

1.7 Second Quantization

1.8 Harmonic Oscillators

1.9 Currents and Second Quantization

1.10 Summary

References

2 Nambu-Goto Strings

2.1 Bosonic Strings

2.2 Gupta-Bleuler Quantization

2.3 Light Cone Quantization

2.4 BRST Quantization

2.5 Trees

2.6 From Path Integrals to Operators

2.7 Projective Invariance and Twists

2.8 Closed Strings

2.9 Ghost Elimination

2.100 Summary

References

3 Superstrings

3.1 Supersymmetric Point Particles

3.2 Two-Dimensional Supersymmetry

3.3 Trees

3.4 Local Two-Dimensional Supersymmetry

3.5 Quantization

3.6 GSO Projection

3.7 Superstrings

3.8 Light Cone Quantization of the GS Action

3.9 Vertices and Trees

3.10 Summary

References

4 Conformal Field Theory and Kac——Moody Algebras

4.1 Conformal Field Theory

4.2 Superconformal Field Theory

4.3 Spin Fields

4.4 Superconformal Ghosts

4.5 Fermion Vertex

4.6 Spinors and Trees

4.7 Kac-Moody Algebras

4.8 Supersymmetry

4.9 Summary

References

5 Mulfiloops and Teichmuller Spaces

5.1 Unitarity

5.2 Single-Loop Amplitude

5.3 Harmonic Oscillators

5.4 Single-Loop Superstring Amplitudes

5.5 Closed Loops

5.6 Multiloop Amplitudes

5.7 Riemann Surfaces and Teichmiiller Spaces

5.8 Conformal Anomaly

5.9 Superstrings

5.10 Determinants and Singularities

5.11 Moduli Space and Grassmannians

5.12 Summary

References

Ⅱ Second Quantization and the Search for Geometry

6 Light Cone Field Theory

6.1 Why String Field Theory?

6.2 Deriving Point Particle Field Theory

6.3 Light Cone Field Theory

6.4 Interactions

6.5 Neumann Function Method

6.6 Equivalence of the Scattering Amplitudes

6.7 Four-String Interaction

6.8 Superstring Field Theory

6.9 Summary

References

7 BRST Field Theory

7.1 Covariant String Field Theory

7.2 BRST Field Theory

7.3 Gauge Fixing

7.4 Interactions

7.5 Witten's String Field Theory

7.6 Proof of Equivalence

7.7 Closed Strings and Superstrings

7.8 Summary

References

Ⅲ Phenomenology and Model Building

8 Anomalies and the Atiyah-Singer Theorem

8.1 Beyond GUT Phenomenology

8.2 Anomalies and Feynman Diagrams

8.3 Anomalies in the Functional Formalism

8.4 Anomalies and Characteristic Classes

8.5 Dirac Index

8.6 Gravitational and Gauge Anomalies

8.7 Anomaly Cancellation in Strings

8.8 Summary

References

9 Heterotic Strings and Compactification

9.1 Compactification

9.2 The Heterotic String

9.3 Spectrum

9.4 Covariant and Fermionic Formulations

9.5 Trees

9.6 Single-Loop Amplitude

9.7 Es and Kac——Moody Algebras

9.8 Lorentzian Lattices

9.9 Summary

References

10 Calabi——Yau Spaces and Orbifolds

10.1 Calabi-Yau Spaces

10.2 Review of de Rahm Cohomology

10.3 Cohomology and Homology

10.4 K/ihler Manifolds

10.5 Embedding the Spin Connection

10.6 Fermion Generations

10.7 Wilson Lines

10.8 Orbifoids

10.9 Four-Dimensional Superstrings

10.10 Summary

References

Ⅳ M-Theory

11 M-Theory and Duality

11.1 Introduction

11.2 Duality in Physics

11.3 Why Five String Theories?

11.4 T-Duality

11.5 S-Duality

11.5.1 Type IIA Theory

11.5.2 Type IIB Theory

11.5.3 M-Theory and Type IIB Theory

11.5.4 E8 E8 Heterotic String

11.5.5 Type I Strings

11.6 Summary

References

12 Compactifications and BPS States

12.1 BPS States

12.2 Supersymmetry and P-Branes

12.3 Compactification

12.4 Example: D = 6

12.4.1 D = 6， N = (2， 2) Theory

12.4.2 D = 6， N = (1， 1) Theories

12.4.3 M-Theory in D = 7

12.5 Example:D=4， N=2 and D=6， N=1

12.6 Symmetry Enhancement and Tensionless Strings

12.7 F-Theory

12.8 Example: D = 4

12.9 Summary

References

13 Solitons， D-Branes， and Black Holes

13.1 Solitons

13.2 Supermembrane Actions

13.3 Five-Brahe Action

13.4 D-Branes

13.5 D-Brane Actions

13.6 M(atrix) Models and Membranes

13.7 Black Holes

13.8 Summary

13.9 Conclusion

References

Appendix

A.1 A Brief Introduction to Group Theory

A.2 A Brief Introduction to General Relativity

A.3 A Brief Introduction to the Theory of Forms

A.4 A Brief Introduction to Supersymmetry

A.5 A Brief Introduction to Supergravity

A.6 Notation

References

Index

超弦和M理论是现代物理学中最有趣最活跃的研究课题之一。该问题比较困难同时也充满争议，一些人称之为“终极理论”，这是因为超弦理论有可能解决困扰人们多年的难题，即统一二十世纪最伟大的两个理论：广义相对论和量子场论。《超弦和M理论导论（第2版）》全面细致地讲解超弦理论和该领域的最新研究进展，内容包括四维超弦，Kac-Moody代数，Teichmuller空间和Calabi-Yau流形，M理论和D膜，对偶和BPS关系，矩阵模型等，可以作为研究生教材，同时对研究人员也有参考价值。作者首先简要介绍了点粒子理论，然后利用费曼路径积分详细讨论超弦理论。超弦研究需要很多数学工具，书中分别作了介绍，如指标定理，同调论和Kahler流形等。在第二版中，作者对内容做了整体修订，并添加了M理论的三个新章节。阅读《超弦和M理论导论（第2版）》需要量子力学和相对论的基本知识。
读者对象：理论物理、高能物理、场论和弦论等专业的高年级本科生、研究生和相关专业的科研人员。