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A First Course in String Theory, Second Edition

Book Description

String theory made understandable. Barton Zwiebach is once again faithful to his goal of making string theory accessible to undergraduates. He presents the main concepts of string theory in a concrete and physical way to develop intuition before formalism, often through simplified and illustrative examples. Complete and thorough in its coverage, this new edition now includes AdS/CFT correspondence and introduces superstrings. It is perfectly suited to introductory courses in string theory for students with a background in mathematics and physics. New sections cover strings on orbifolds, cosmic strings, moduli stabilization, and the string theory landscape. Now with almost 300 problems and exercises, with password-protected solutions for instructors at www.cambridge.org/zwiebach.

Note:The ebook version does not provide access to the companion files.

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Dedication
  5. Contents
  6. Foreword by David Gross
  7. From the Preface to the First Edition
  8. Preface to the Second Edition
  9. Part I: Basics
    1. 1. A brief introduction
      1. 1.1 The road to unification
      2. 1.2 String theory as a unified theory of physics
      3. 1.3 String theory and its verification
      4. 1.4 Developments and outlook
    2. 2. Special relativity and extra dimensions
      1. 2.1 Units and parameters
      2. 2.2 Intervals and Lorentz transformations
      3. 2.3 Light-cone coordinates
      4. 2.4 Relativistic energy and momentum
      5. 2.5 Light-cone energy and momentum
      6. 2.6 Lorentz invariance with extra dimensions
      7. 2.7 Compact extra dimensions
      8. 2.8 Orbifolds
      9. 2.9 Quantum mechanics and the square well
      10. 2.10 Square well with an extra dimension
    3. 3. Electromagnetism and gravitation in various dimensions
      1. 3.1 Classical electrodynamics
      2. 3.2 Electromagnetism in three dimensions
      3. 3.3 Manifestly relativistic electrodynamics
      4. 3.4 An aside on spheres in higher dimensions
      5. 3.5 Electric fields in higher dimensions
      6. 3.6 Gravitation and Planck's length
      7. 3.7 Gravitational potentials
      8. 3.8 The Planck length in various dimensions
      9. 3.9 Gravitational constants and compactification
      10. 3.10 Large extra dimensions
    4. 4. Nonrelativistic strings
      1. 4.1 Equations of motion for transverse oscillations
      2. 4.2 Boundary conditions and initial conditions
      3. 4.3 Frequencies of transverse oscillation
      4. 4.4 More general oscillating strings
      5. 4.5 A brief review of Lagrangian mechanics
      6. 4.6 The nonrelativistic string Lagrangian
    5. 5. The relativistic point particle
      1. 5.1 Action for a relativistic point particle
      2. 5.2 Reparameterization invariance
      3. 5.3 Equations of motion
      4. 5.4 Relativistic particle with electric charge
    6. 6. Relativistic strings
      1. 6.1 Area functional for spatial surfaces
      2. 6.2 Reparameterization invariance of the area
      3. 6.3 Area functional for spacetime surfaces
      4. 6.4 The Nambu-Goto string action
      5. 6.5 Equations of motion, boundary conditions, and D-branes
      6. 6.6 The static gauge
      7. 6.7 Tension and energy of a stretched string
      8. 6.8 Action in terms of transverse velocity
      9. 6.9 Motion of open string endpoints
    7. 7. String parameterization and classical motion
      1. 7.1 Choosing a σ parameterization
      2. 7.2 Physical interpretation of the string equation of motion
      3. 7.3 Wave equation and constraints
      4. 7.4 General motion of an open string
      5. 7.5 Motion of closed strings and cusps
      6. 7.6 Cosmic strings
    8. 8. World-sheet currents
      1. 8.1 Electric charge conservation
      2. 8.2 Conserved charges from Lagrangian symmetries
      3. 8.3 Conserved currents on the world-sheet
      4. 8.4 The complete momentum current
      5. 8.5 Lorentz symmetry and associated currents
      6. 8.6 The slope parameter α′
    9. 9. Light-cone relativistic strings
      1. 9.1 A class of choices for τ
      2. 9.2 The associated σ parameterization
      3. 9.3 Constraints and wave equations
      4. 9.4 Wave equation and mode expansions
      5. 9.5 Light-cone solution of equations of motion
    10. 10. Light-cone fields and particles
      1. 10.1 Introduction
      2. 10.2 An action for scalar fields
      3. 10.3 Classical plane-wave solutions
      4. 10.4 Quantum scalar fields and particle states
      5. 10.5 Maxwell fields and photon states
      6. 10.6 Gravitational fields and graviton states
    11. 11. The relativistic quantum point particle
      1. 11.1 Light-cone point particle
      2. 11.2 Heisenberg and Schrödinger pictures
      3. 11.3 Quantization of the point particle
      4. 11.4 Quantum particle and scalar particles
      5. 11.5 Light-cone momentum operators
      6. 11.6 Light-cone Lorentz generators
    12. 12. Relativistic quantum open strings
      1. 12.1 Light-cone Hamiltonian and commutators
      2. 12.2 Commutation relations for oscillators
      3. 12.3 Strings as harmonic oscillators
      4. 12.4 Transverse Virasoro operators
      5. 12.5 Lorentz generators
      6. 12.6 Constructing the state space
      7. 12.7 Equations of motion
      8. 12.8 Tachyons and D-brane decay
    13. 13. Relativistic quantum closed strings
      1. 13.1 Mode expansions and commutation relations
      2. 13.2 Closed string Virasoro operators
      3. 13.3 Closed string state space
      4. 13.4 String coupling and the dilaton
      5. 13.5 Closed strings on the R1/Z2 orbifold
      6. 13.6 The twisted sector of the orbifold
    14. 14. A look at relativistic superstrings
      1. 14.1 Introduction
      2. 14.2 Anticommuting variables and operators
      3. 14.3 World-sheet fermions
      4. 14.4 Neveu−Schwarz sector
      5. 14.5 Ramond sector
      6. 14.6 Counting states
      7. 14.7 Open superstrings
      8. 14.8 Closed string theories
  10. Part II: Developments
    1. 15. D-branes and gauge fields
      1. 15.1 D p-branes and boundary conditions
      2. 15.2 Quantizing open strings on Dp-branes
      3. 15.3 Open strings between parallel Dp-branes
      4. 15.4 Strings between parallel Dp- and Dq-branes
    2. 16. String charge and electric charge
      1. 16.1 Fundamental string charge
      2. 16.2 Visualizing string charge
      3. 16.3 Strings ending on D-branes
      4. 16.4 D-brane charges
    3. 17. T-duality of closed strings
      1. 17.1 Duality symmetries and Hamiltonians
      2. 17.2 Winding closed strings
      3. 17.3 Left movers and right movers
      4. 17.4 Quantization and commutation relations
      5. 17.5 Constraint and mass formula
      6. 17.6 State space of compactified closed strings
      7. 17.7 A striking spectrum coincidence
      8. 17.8 Duality as a full quantum symmetry
    4. 18. T-duality of open strings
      1. 18.1 T-duality and D-branes
      2. 18.2 U (1) gauge transformations
      3. 18.3 Wilson lines on circles
      4. 18.4 Open strings and Wilson lines
    5. 19. Electromagnetic fields on D-branes
      1. 19.1 Maxwell fields coupling to open strings
      2. 19.2 D-branes with electric fields
      3. 19.3 D-branes with magnetic fields
    6. 20. Nonlinear and Born–Infeld electrodynamics
      1. 20.1 The framework of nonlinear electrodynamics
      2. 20.2 Born−Infeld electrodynamics
      3. 20.3 Born−Infeld theory and T-duality
    7. 21. String theory and particle physics
      1. 21.1 Intersecting D6-branes
      2. 21.2 D-branes and the Standard Model gauge group
      3. 21.3 Open strings and the Standard Model fermions
      4. 21.4 The Standard Model on intersecting D6-branes
      5. 21.5 String theory models of particle physics
      6. 21.6 Moduli stabilization and the landscape
    8. 22. String thermodynamics and black holes
      1. 22.1 A review of statistical mechanics
      2. 22.2 Partitions and the quantum violin string
      3. 22.3 Hagedorn temperature
      4. 22.4 Relativistic particle partition function
      5. 22.5 Single string partition function
      6. 22.6 Black holes and entropy
      7. 22.7 Counting states of a black hole
    9. 23. Strong interactions and AdS/CFT
      1. 23.1 Introduction
      2. 23.2 Mesons and quantum rotating strings
      3. 23.3 The energy of a stretched effective string
      4. 23.4 A large-N limit of a gauge theory
      5. 23.5 Gravitational effects of massive sources
      6. 23.6 Motivating the AdS/CFT correspondence
      7. 23.7 Parameters in the AdS/CFT correspondence
      8. 23.8 Hyperbolic spaces and conformal boundary
      9. 23.9 Geometry of AdS and holography
      10. 23.10 AdS/CFT at finite temperature
      11. 23.11 The quark–gluon plasma
    10. 24. Covariant string quantization
      1. 24.1 Introduction
      2. 24.2 Open string Virasoro operators
      3. 24.3 Selecting the quantum constraints
      4. 24.4 Lorentz covariant state space
      5. 24.5 Closed string Virasoro operators
      6. 24.6 The Polyakov string action
    11. 25. String interactions and Riemann surfaces
      1. 25.1 Introduction
      2. 25.2 Interactions and observables
      3. 25.3 String interactions and global world-sheets
      4. 25.4 World-sheets as Riemann surfaces
      5. 25.5 Schwarz−Christoffel map and three-string interaction
      6. 25.6 Moduli spaces of Riemann surfaces
      7. 25.7 Four open string interaction
      8. 25.8 Veneziano amplitude
    12. 26. Loop amplitudes in string theory
      1. 26.1 Loop diagrams and ultraviolet divergences
      2. 26.2 Annuli and one-loop open strings
      3. 26.3 Annuli and electrostatic capacitance
      4. 26.4 Non-planar open string diagrams
      5. 26.5 Four closed string interactions
      6. 26.6 The moduli space of tori
  11. References
  12. Index