David Tong: Gauge Theory

David Tong: Lectures on Gauge Theory

These lecture notes provide an introduction to the basic physics of non-Abelian gauge theories in four dimensions, and other strongly coupled field theories in lower dimensions. They are aimed at beginning graduate students. The lecture notes are long (around 400 pages), but bite-sized chunks can be downloaded below.



  • 1. Topics in Electromagnetism:   PDF
    Introduction; Magnetic monopoles, Dirac quantisation; The theta term, Topological insulators, The Witten effect.
  • 2. Yang-Mills Theory:   PDF
    Introducing Yang-Mills. Wilson lines and Wilson loops; The theta term, Canonical quantisation; Instantons, Tunnelling; RG, Anti-screening and paramagnetism, The beta function; Confinement, Superconductivity; 't Hooft lines; Infra-red phases of QCD, The Higgs vs confining phase; 't Hooft Polyakov monopoles, the Witten effect again.
  • 3. Anomalies:   PDF
    The chiral anomaly in two dimensions and four dimensions; Noethers theorem and Ward identities, Fujikawa's approach and the measure, Triangle diagrams, Mixed gravitational anomalies; Fermi zero modes, The Atiyah-Singer index theorem, Instantons again, Topological Insulators again; Gauge anomalies; The SU(2) anomaly, Anomaly cancellation and the Standard Model; 't Hooft Anomalies; Anomalies in discrete symmetries, Generalised symmetries, Time-Reversal.
  • 4 Lattice Gauge Theory:   PDF
    Scalar fields; Gauge fields, The Wilson action, the Haar measure, the strong coupling expansion; Fermions, The Nielsen-Ninomiya theorem, Lattice QCD; Domain wall fermions, Anomaly inflow, the Ginsparg-Wilson relation.
  • 5. Chiral Symmetry Breaking:   PDF
    The quark condensate; The chiral Lagrangian, Pion scattering, Currents; Baryons, The Skyrme model, Skyrmions; QCD and its mesons and baryons; the Wess-Zumino Witten WZW term, A five dimensional action; 't Hooft anomaly matching; Confinement and chiral symmetry breaking; The Vafa-Witten theorem, Massless baryons.
  • 6. Large N:   PDF
    An atomic warm-up; Large N Yang-Mills is a string theory, glueball scattering and decay, The theta angle; Large N QCD, mesons, baryons; The chiral lagrangian revisisted, the eta-prime, the Witten-Veneziano formula.
  • 7. Quantum Field Theory in Two Dimensions:   PDF
    Electromagnetism in two dimensions, The theta angle as a background electric field; The Abelian-Higgs model, vortices; The CP^N model, confinement, instantons; The Gross-Neveu model, The chiral Gross-Neveu model; Bosonization, Massive Thirring and the Sine-Gordon model, the Schwinger model; Non-Abelian bosonization, the WZW term.
  • 8. Quantum Field Theory in Three Dimensions:   PDF
    Electromagnetism in three dimensions, Monopole operators; The Abelian-Higgs model and particle-vortex duality; Polyakov's model of confinement, monopoles as instantons; Chern-Simons theory; Fermions and the parity anomaly; Bosonization, Flux attachment, The duality web.

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