TASI Lectures on Solitons
Abstract
Description
These lectures cover aspects of solitons with focus on applications to the quantum dynamics of supersymmetric gauge theories and string theory. The lectures consist of four sections, each dealing with a different soliton. We start with instantons and work down in co-dimension to monopoles, vortices and, eventually, domain walls. Emphasis is placed on the moduli space of solitons and, in particular, on the web of connections that links solitons of different types. The D-brane realization of the ADHM and Nahm construction for instantons and monopoles is reviewed, together with related constructions for vortices and domain walls. Each lecture ends with a series of vignettes detailing the roles solitons play in the quantum dynamics of supersymmetric gauge theories in various dimensions. This includes applications to the AdS/CFT correspondence, little string theory, S-duality, cosmic strings, and the quantitative correspondence between 2d sigma models and 4d gauge theories.
139 (small) pages. Lots of figures. This is an extended write up of lectures given at TASI, June 2005. v2-5: typos corrected, references added
139 (small) pages. Lots of figures. This is an extended write up of lectures given at TASI, June 2005. v2-5: typos corrected, references added