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.
Content : Soliton Lecture Notes
- 1. Instantons:
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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
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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:
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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:
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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.
Solitons on the Web
- Calculus of Many Instantons: by Dorey, Hollowood, Khoze and Mattis. Includes the ADHM construction and applications to supersymmetric gauge theories.
- Instantons and Supersymmetry: by Shifman and Vainshtein.
- Monopoles and Duality: by Harvey.
- Duality for Children: by Figueroa-O'Farrill. Covers monopoles and their application to understanding S-duality.
- Vortices and Monopoles: An older review by Preskill available from KEK.
- Cosmic Strings: by Polchinski.