David Tong: Solitons

David Tong: TASI Lectures on Solitons

These lectures were given at the Theoretical Advanced Study Institute, University of Colorado, Boulder in June 2005. They are aimed at advanced graduate students and cover solitons in gauge theories, with emphasis on applications to string theory and supersymmetric gauge dynamics. The notes were last updated in September 2005 and are now also available on the arxiv. The full lecture notes weigh in at around 140 (small, American) pages. For those that prefer bite size chunks, individual chapters can be found below.


PDF

Content : Soliton Lecture Notes


  • 1. Instantons: PDF
    The self-dual Yang-Mills equations; Solutions and collective coordinates; Instanton moduli spaces; Fermi zero modes; ADHM construction; Applications: the AdS/CFT correspondence, (2,0) theory in six dimensions.

  • 2. Monopoles PDF
    Dirac quantization; Monopole equations; Solutions and collective coordinates; Monopole moduli spaces; Dyons; Nahm's equations; Applications: monopoles in three dimensions, S-duality, monopole strings, d-branes in little string theory.

  • 3. Vortices: PDF
    Vortex equations; Vortex moduli spaces; Brane constructions; Relationship to instantons; Vortices and lumps; Applications: vortices and mirror symmetry, swapping vortices and electrons, cosmic strings.

  • 4. Domain Walls: PDF
    Domain wall equations; Domain wall moduli spaces; Ordering of domain walls; Effect on vortices; Relationship to monopoles; Brane construction; Applications: the sigma-model gauge theory correspondence, 2d black holes, field theoretic D-branes.


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