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
1.3String 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
1.5Other 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
1.6Conclusion
2 Free bosonic strings
2.1The 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
2.2Quantization - 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
3.1Covariant path-integral quantization
3.1.1 Fazideev-P0pov ghosts
3.1.2 Complex world-sheet tensor calculus
3.1.3 Quantizatlon of the ghosts3.2.1 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
3.3Global aspects of the string world sheet
3.4Strings 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
3.5Summary
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
4.2Quantization - 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
4.6Summary
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-Poincar
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
6.1Open 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
6.3Heterotic strings
6.3.1 The SO(32) theory
6.3.2 The Es x Es theory
6.4Toroidal 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
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