Recent years have brought a revival of work on string theory, which has been a source of fascination since its origins nearly twenty years ago.There seems to be a widely perceived need for a systematic, pedagogical exposition of the present state of knowledge about string theory. We hope that this book will help to meet this need. To give a comprehensive account of such a vast topic as string theory would scarcely be possible,even in two volumes with the length to which these have grown. Indeed,we have had to omit many important subjects, while treating others only sketchily. String field theory is omitted entirely (though the subject of chapter 11 is closely related to light-cone string field theory). Conformal field theory is not developed systematically, though much of the background material needed to understand recent papers on this subject is presented in chapter 3 and elsewhere.

Preface

1   Introduction

1.1  The early days of dual models

1.1.1 The Veneziano amplitude and duality

1.1.2 High-energy behavior of the Veneziano model

1.1.3 Ramifications of the Veneziano model

1.2  Dual models of everything

1.2.1 Duality and the graviton

1.2.2 Unification in higher dimensions

1.2.3 Supersymmetry

1.3  String theory

1.3.1 The massless point particle

1.3.2 Generalization to strings

1.3.3 Constraint equations

1.4  String interactions

4.1 Splitting of strings

1.4.2 Vertex operators

1.4.3 Use of vertex operators

1.4.4 Evaluation of the scattering amplitude

1.4.5 The mass of the graviton

1.5  Other aspects of string theory

1.5.1 Gravitational Ward identities

1.5.2 Open strings

1.5.3 Internal symmetries of open strings

1.5.4 Recovery of the Veneziano amplitude

1.5.5 Comparison with QCD

  1.5.6 Upitarity and gravity

1.6  Conclusion

2   Free bosonic strings

2.1  The classical bosonic string

2.1.1 String action and its symmetries

2.1.2 The free string in Minkowski space

2.1.3 Classical covariant gauge fixing and field equations

2.2  Quantization - old covariant approach

2.2.1 Commutation relations and mode expansions

2.2.2 Virasoro algebra and physical states

2.2.3 Vertex operators

2.3  Light-cone gauge quantization

2.3.1 Light-cone gauge and Lorentz algebra

2.3.2 Construction of transverse physical states

2.3.3 The no-ghost theorem and the spectrum-generating algebra

2.3.4 Analysis of the spectrum

2.3.5 Asymptotic formulas for level densities

2.4  Summary

3   Modern covariant quantization

3.1  Covariant path-integral quantization

3.1.1 Fazideev-P0pov ghosts

3.1.2 Complex world-sheet tensor calculus

3.1.3 Quantizatlon of the ghosts

3.2  BRST quantization

3.2.1 Construction of BRST charge

3.2.2 Covariant calculation of the Virasoro anomaly

3.2.3 Virasoro, conformal and gravitational anomalies

3.2.4 Bosonization of ghost coordinates

3.3  Global aspects of the string world sheet

3.4  Strings in background fields

3.4.1 Introduction of a background spa~e-time metric

3.4.2 Weyl invariance

3.4.3 Conformal invariance and the equations of motion

3.4.4 String-theoretic corrections to general relativity

3.4.5 Inclusion of other modes

3.4.6 The dilaton expectation value and the string coupling constant

3.5  Summary

4   World-sheet supersymmetry in string theory

4.1  The classical theory

4.1.1 Global world-sheet supersymmetry

4.1.2 Superspace

4.1.3 Constraint equations

4.1.4 Boundary conditions and mode expansions

4.2  Quantization - the old covariant approach

4.2.1 Commutation relations and mode expansions

4.2.2 Super-Virasoro algebra and physical states

4.2.3 Boson-emission vertex operators

4.3  Light-cone gauge quantization

4.3.1 The light-cone gauge

4.3.2 No-ghost theorem and

the spectrum-generating algebra

4.3.3 The GSO conditions

4.3.4 Locally supersymmetric form of the action

4.3.5 Superstring action and its symmetries

4.4  Modern covariant quantization

4.4.1 Faddeev-Popov ghosts

4.4.2 BRST symmetry

4.4.3 Covariant computation of the Virasoro anomaly

4.5  Extended world-sheet supersymmetry

4.5.1 The N = 2 theory

4.5.2 The N = 4 theory

4.6  Summary

4.A  Super Yang-Mills theories

5   Space-time supersymmetry in string theory

5.1  The classical theory

5.1.1 The superparticle

5.1.2 The supersymmetric string action

5.1.3 The local fermionic symmetry

5.1.4 Type I and type II superstrings

5.2  Quantization

5.2.1 Light-cone gauge

5.2.2 Super-Poincard algebra

5.3  Analysis of the spectrum

5.3.1 Open superstrings

5.3.2 Closed superstrings

5.4  Remarks concerning covariant quantization

5.5  Summary

5.A  Properties of SO(2n) groups

5.B  The spin(8) Clifford algebra

6   Nonabelian gauge symmetry

6.1  Open strings

6.1.1 The Chan-Paton method

6.1.2 Allowed gauge groups and:representations

6.2  Current algebra on' the string world sheet

6.3  Heterotic strings

6.3.1 The SO(32) theory

6.3.2 The Es x Es theory

6.4  Toroidal compactification

6.4.1 Compactification on a circle

6.4.2 Fermionization

6.4.3 Bosonized description of the heterotic string

6.4.4 Vertex operator representations

6.4.5 Formulas for the cocycles

6.4.6 The full current Mgebra

6.4.7 The Es and spin(32)/Z2 lattices

6.4.8 The heterotic string spectrum

6.5  Summary

6.A  Elements of Es

6.B  Modular forms

7   Tree amplitudes

7.1  Bosonic open strings

7.1.1 The structure of tree amplitudes

7.1.2 Decoupling of ghosts

7.1.3 Cyclic symmetry

7.1.4 Examples

7.1.5 Tree-level gauge invariance

7.1.6 The twist operator

7.2  Bosonic closed strings

7.2.1 Construction of tree amplitudes

7.2.2 Examples

7.2.3 Relationship to open-string trees

7.3  Superstrings in the RNS formulation

7.3.1 Open-string tree amplitudes in the bosonic sector

7.3.2 The F1 picture

7.3.3 Examples

7.3.4 Tree amplitudes with one fermion line

7.3.5 Fermion-emission vertices

7.4  Superstrings in the supersymmetric formulation

7.4.1 Massless particle vertices

7.4.2 Open-string trees

7.4.3 Closed-string trees

7.4.4 Heterotic-string trees

7.5  Summary

7.A  Coherent-state methods and correlation functions

Bibliography

Index