TASI Lectures on Solitons

TL;DR

This series of lectures explores various solitons, their moduli spaces, and their roles in supersymmetric gauge theories and string theory, highlighting their interconnectedness and applications in quantum dynamics.

Contribution

Provides a comprehensive review of solitons, including instantons, monopoles, vortices, and domain walls, with emphasis on their moduli spaces and D-brane realizations in supersymmetric theories.

Findings

Connections between different solitons are elucidated.

D-brane constructions for solitons are reviewed.

Applications to AdS/CFT and S-duality are discussed.

Abstract

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.