弦論

This is a textbook on the collection ofideas categorized under the name of "string theory." This is a large domain that has as its central goal the unification ofallinteractions including gravity. There have been several surges ofprogress in different directions in the past twenty years， and this book tries to give the student ofthe field some of the salientideas.

1 Introduction

1.i Prehistory

1.2 The Case for String Theory

1.3 A Stringy Historical Perspective

1.4 Conventions

Bibliography

2 Classical String Theory

2.1 The Point Particle

2.2 Relativistic Strings

2.3 0scillator Expansions

2.3.1 00sed strings

2.3.2 0pen strings

2.3.3 The Virasoro constraints

Bibliography

Exercises

3 Quantization of Bosonic Strings

3.1 Covariant Canonical Quantization

3.2 Light-cone Quantization

3.3 Spectrum of the Bosonic String

3.4 Unoriented Strings

3.4. 1 0pen. strings and Chan-Patonfactors

3.5 Path Integral Quantization

3.6 Topologically Nontrivial World-sheets

3.7 BRST Primer

3.8 BRST in String Theory and the Physical Spectrum

Bibliography

Exercises

4 Conformal Field Theory

4.1 Conformal Transformations

4.1.1 The case oftwo dimensions

4.2 Conformally Invariant Field Theory

4.3 Radial Quantization

4.4 Mode Expansions

4.5 The Virasoro Algebra and the Central Charge

4.6 The Hilbert Space

4.7 The Free Boson

4.8 The Free Fermion

4.9 The Conformal Anomaly

4.10 Representations of the Conformal Algebra

4.11 Affine Current Algebras

4.12 Free Fermions and O(N) Affine Symmetry

4.13 Superconformal Symmetry

4.13.1 N =(1.0)2 SIAperconformal symmetry

4.13.2 N =(2.0)2 superconformal symmetry

4.13.3 N =(4.0)2 superconformal symmetry

4.14 Scalars with Background Charge

4.15 The CFT of Ghosts

4.16 CFT on the Disk

4.16.1 Free massless bosons on the dislc

4.16.2 Free masslessfern竹ions on the dislc

4.16.3 The projective plane

4.17 CFT on the Torus

4.18 Compact Scalars

4.18.1 Modular invariance

4.18.2 Decompaaification

4.18.3 The torus propagator

4.18.4 Marginal deformations

4.18.5 Multiple compaa scalars

4.18.6 Enhanced symmetry and the string Brout-Englert-lliggs effea

4.18.7 T-duality

4.19 Free Fermions on the Torus

4.20 Bosonization

4.20. 1 "Bosonization " of bosonic ghost system

4.21 0rbifolds

……

5 Scattering Amplitudes and 'Vertex Operators

6 Strings in Background Fields

7 Superstrings and Supersymmetry

8 D-branes

9 Compactifications and Supersymmetry Breaking

10 Loop Corrections to String Effective Couplings

11 Duality Connections and Nonperturbative Effects

12 Black Holes and Entropy in String Theory

13 The Bulk／Boundary Correspondence

14 String theroy and Matrix Models