Solitons and D-Branes
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. They are also available on the arXiv. The full lecture notes weigh in at around 140 pages. For those that prefer bite size chunks, individual chapters can be found below.
“Instantons, monopoles, vortices and kinks; These are a few of my favorite things.”
Maria von Trapp (deleted scene)
Instantons
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.
Monopoles
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.
Vortices
Vortex equations; Vortex moduli spaces; Brane constructions; Relationship to instantons; Vortices and lumps; Applications: vortices and mirror symmetry, swapping vortices and electrons, cosmic strings.
Domain Walls
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.