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Superstring Theory

Book Description

Twenty-five years ago, Michael Green, John Schwarz, and Edward Witten wrote two volumes on string theory. Published during a period of rapid progress in this subject, these volumes were highly influential for a generation of students and researchers. Despite the immense progress that has been made in the field since then, the systematic exposition of the foundations of superstring theory presented in these volumes is just as relevant today as when first published. A self-contained introduction to superstrings, Volume 1 begins with an elementary treatment of the bosonic string, before describing the incorporation of additional degrees of freedom: fermionic degrees of freedom leading to supersymmetry and internal quantum numbers leading to gauge interactions. A detailed discussion of the evaluation of tree-approximation scattering amplitudes is also given. Featuring a new Preface setting the work in context in light of recent advances, this book is invaluable for graduate students and researchers in general relativity and elementary particle theory.

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. Preface to the 25th Anniversary Edition
  6. 1. Introduction
    1. 1.1 The early days of dual models
      1. 1.1.1 The Veneziano amplitude and duality
      2. 1.1.2 High-energy behavior of the Veneziano model
      3. 1.1.3 Ramifications of the Veneziano model
    2. 1.2 Dual models of everything
      1. 1.2.1 Duality and the graviton
      2. 1.2.2 Unification in higher dimensions
      3. 1.2.3 Supersymmetry
    3. 1.3 String Theory
      1. 1.3.1 The massless point particle
      2. 1.3.2 Generalization to strings
      3. 1.3.3 Constraint equations
    4. 1.4 String interactions
      1. 1.4.1 Splitting of strings
      2. 1.4.2 Vertex operators
      3. 1.4.3 Use of vertex operators
      4. 1.4.4 Evaluation of the scattering amplitude
      5. 1.4.5 The mass of the graviton
    5. 1.5 Other aspects of string theory
      1. 1.5.1 Gravitational Ward identities
      2. 1.5.2 Open strings
      3. 1.5.3 Internal symmetries of open strings
      4. 1.5.4 Recovery of the Veneziano amplitude
      5. 1.5.5 Comparison with QCD
      6. 1.5.6 Unitarity and gravity
    6. 1.6 Conclusion
  7. 2. Free bosonic strings
    1. 2.1 The classical bosonic string
      1. 2.1.1 String action and its symmetries
      2. 2.1.2 The free string in Minkowski space
      3. 2.1.3 Classical covariant gauge fixing and field equations
    2. 2.2 Quantization – old covariant approach
      1. 2.2.1 Commutation relations and mode expansions
      2. 2.2.2 Virasoro algebra and physical states
      3. 2.2.3 Vertex operators
    3. 2.3 Light-cone gauge quantization
      1. 2.3.1 Light-cone gauge and Lorentz algebra
      2. 2.3.2 Construction of transverse physical states
      3. 2.3.3 The no-ghost theorem and the spectrum-generating algebra
      4. 2.3.4 Analysis of the spectrum
      5. 2.3.5 Asymptotic formulas for level densities
    4. 2.4 Summary
  8. 3. Modern covariant quantization
    1. 3.1 Covariant path-integral quantization
      1. 3.1.1 Faddeev-Popov ghosts
      2. 3.1.2 Complex world-sheet tensor calculus
      3. 3.1.3 Quantization of the ghosts
    2. 3.2 BRST quantization
      1. 3.2.1 Construction of the BRST charge
      2. 3.2.2 Covariant calculation of the Virasoro anomaly
      3. 3.2.3 Virasoro, conformal and gravitational anomalies
      4. 3.2.4 Bosonization of ghost coordinates
    3. 3.3 Global aspects of the string world sheet
    4. 3.4 Strings in background fields
      1. 3.4.1 Introduction of a background space-time metric
      2. 3.4.2 Weyl invariance
      3. 3.4.3 Conformal invariance and the equations of motion
      4. 3.4.4 String-theoretic corrections to general relativity
      5. 3.4.5 Inclusion of other modes
      6. 3.4.6 The dilaton expectation value and the string coupling constant
    5. 3.5 Summary
  9. 4. World-sheet supersymmetry in string theory
    1. 4.1 The classical theory
      1. 4.1.1 Global world-sheet supersymmetry
      2. 4.1.2 Superspace
      3. 4.1.3 Constraint equations
      4. 4.1.4 Boundary conditions and mode expansions
    2. 4.2 Quantization - the old covariant approach
      1. 4.2.1 Commutation relations and mode expansions
      2. 4.2.2 Super-Virasoro algebra and physical states
      3. 4.2.3 Boson-emission vertex operators
    3. 4.3 Light-cone gauge quantization
      1. 4.3.1 The light-cone gauge
      2. 4.3.2 No-ghost theorem and the spectrum-generating algebra
      3. 4.3.3 The GSO conditions
      4. 4.3.4 Locally supersymmetric form of the action
      5. 4.3.5 Superstring action and its symmetries
    4. 4.4 Modern covariant quantization
      1. 4.4.1 Faddeev-Popov ghosts
      2. 4.4.2 BRST Symmetry
      3. 4.4.3 Covariant computation of the Virasoro anomaly
    5. 4.5 Extended world-sheet supersymmetry
      1. 4.5.1 The N = 2 theory
      2. 4.5.8 The N = 4 theory
    6. 4.6 Summary
    7. 4.A Super Yang–Mills theories
  10. 5. Space-time supersymmetry in string theory
    1. 5.1 The classical theory
      1. 5.1.1 The superparticle
      2. 5.1.2 The supersymmetric string action
      3. 5.1.3 The local fermionic symmetry
      4. 5.1.4 Type I and type II superstrings
    2. 5.2 Quantization
      1. 5.2.1 Light-cone gauge
      2. 5.2.2 Super-Poincaré algebra
    3. 5.3 Analysis of the spectrum
      1. 5.3.1 Open superstrings
      2. 5.3.2 Closed superstrings
    4. 5.4 Remarks concerning covariant quantization
    5. 5.5 Summary
    6. 5.A Properties of SO(2n) groups
    7. 5.B The spin(8) Clifford algebra
  11. 6. Nonabelian gauge symmetry
    1. 6.1 Open strings
      1. 6.1.1 The Chan–Paton method
      2. 6.1.2 Allowed gauge groups and representations
    2. 6.2 Current algebra on the string world sheet
    3. 6.3 Heterotic strings
      1. 6.3.1 The SO(32) theory
      2. 6.3.2 The E8 × E8 theory
    4. 6.4 Toroidal compactification
      1. 6.4.1 Compactification on a circle
      2. 6.4.2 Fermionization
      3. 6.4.3 Bosonized description of the heterotic string
      4. 6.4.4 Vertex operator representations
      5. 6.4.5 Formulas for the cocycles
      6. 6.4.6 The full current algebra
      7. 6.4.7 The E8 and spin(32)/Z2 lattices
      8. 6.4.8 The heterotic string spectrum
    5. 6.5 Summary
    6. 6.A Elements of E8
    7. 6.B Modular forms
  12. 7. Tree Amplitudes
    1. 7.1 Bosonic open strings
      1. 7.1.1 The structure of tree amplitudes
      2. 7.1.2 Decoupling of ghosts
      3. 7.1.3 Cyclic symmetry
      4. 7.1.4 Examples
      5. 7.1.5 Tree-level gauge invariance
      6. 7.1.6 The twist operator
    2. 7.2 Bosonic closed strings
      1. 7.2.1 Construction of tree amplitudes
      2. 7.2.2 Examples
      3. 7.2.3 Relationship to open-string trees
    3. 7.3 Superstrings in the RNS formulation
      1. 7.3.1 Open-string tree amplitudes in the bosonic sector
      2. 7.3.2 The F1 picture
      3. 7.3.3 Examples
      4. 7.3.4 Tree amplitudes with one fermion line
      5. 7.3.5 Fermion-emission vertices
    4. 7.4 Superstrings in the supersymmetric formulation
      1. 7.4.1 Massless particle vertices
      2. 7.4.2 Open-string trees
      3. 7.4.3 Closed-string trees
      4. 7.4.4 Heterotic string trees
    5. 7.5 Summary
    6. 7.A Coherent-state methods and correlation functions
  13. Bibliography
  14. Index