David Tong: String Theory

David Tong: Lectures on String Theory

These lecture notes provide a detailed introduction to the bosonic string and conformal field theory, aimed at "Part III" (i.e. masters level) students. The full set of lectures notes can be downloaded here and weigh in at around 200 pages. They are now also available on the arxiv. Individual sections can be downloaded below. Last updated February 2012.



  • 0. Introduction:   Postscript    PDF
    Table of Contents; Why study string theory? Aspects of quantum gravity.
  • 1. The Classical String:   Postscript    PDF
    Point Particles, Nambu-Goto Action, Polyakov Action, Weyl Invariance, Mode Expansions.
  • 2. The Quantum String:   Postscript    PDF
    Covariant Quantization; Lightcone Quantization; String Spectrum, Tachyons and Gravitons.
  • 3. Open Strings and D-Branes:   Postscript    PDF
    D-branes; Quantization and a World of Light; Brane Dynamics; Multiple Branes and a World of Glue.
  • 4. Introducing Conformal Field Theory:   Postscript    PDF
    Noether Currents; Operator Product Expansion; Ward Identities; Central Charge, Weyl Anomaly; Radial Quantization; Virasoro Algebra; State-Operator Map.
  • 5. Path Integrals and Ghosts:   Postscript    PDF
    The Path Integral; The Ghost CFT; Critical Dimension; States and Vertex Operators.
  • 6. Scattering Amplitudes:   Postscript    PDF
    What to Compute? The S-matrix; Summing over Topologies; Virasoro-Shapiro Amplitude; Veneziano Amplitude; Moduli Space of the Torus; One-Loop Partition Function; Integrals and Gamma Functions.
  • 7. Low Energy Effective Actions:   Postscript    PDF
    Einstein's Equations, the Beta Function and Ricci Flow; The B-field and the Dilaton; Low Energy Effective Action; Simple Solutions: the String, the Magnetic Brane, the Linear Dilaton; Background Gauge Fields; DBI Action; Yang-Mills.
  • 8. Compactification and T-Duality:   Postscript    PDF
    Kaluza-Klein Compactification; Enhanced Gauge Symmetries; Why Big Circles are the Same as Small Circles.

Problem Sheets

  • Problem Sheet 1:   Postscript    PDF    Classical and Quantum Strings

  • Problem Sheet 2:   Postscript    PDF    Conformal Field Theory

  • Problem Sheet 3:   Postscript    PDF    Mostly Scattering Amplitudes

  • Problem Sheet 4:   Postscript    PDF    Background Fields

String Theory on the Web