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TASI Lectures on Solitons
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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.
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Cited by 7 Pith papers
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Non-relativistic limits of $\mathcal N=4$ supersymmetric Yang-Mills theory and S-duality
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Dyon Loops and Abelian Instantons
Abelian instantons generated by dyon loops carry full instanton charge in the Georgi-Glashow model and form a continuous deformation of small BPST instantons.
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Unified description of color-electric and color-magnetic strings in hybrid vacua of $\mathcal{N}=2$ supersymmetric QCD
Exact twisted superpotential on non-Abelian string world sheets in hybrid r-vacua yields precise matching of 2D kink masses to 4D confined monopoles and quarks.
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Phase-dependent kink collisions and dual critical-velocity branches in the complex sine-Gordon model
In the complex sine-Gordon model, kink collisions exhibit two phase-dependent critical-velocity branches — one where higher speed causes capture, one where higher speed causes scattering.
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D-branes and fractional instantons on a twisted four torus: the moduli space as an N=2 supersymmetric Higgs branch
The local moduli space of self-dual fractional instantons (Q = r/N) on a twisted four-torus is the Higgs branch of an N=2 supersymmetric theory, obtained via wrapped intersecting D-brane configurations.
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Harmonic Superspace for Ali-Ilahi's ADHM Instanton Sigma Model
The authors build a dual harmonic superspace and write the off-shell (0,4) superspace actions, interactions, and ADHM instanton gauge field for the complementary ADHM instanton sigma model.
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From the Great Wave of Translation to the Force between Quarks
Solitons from the KdV equation yield reflectionless potentials that approximate confining forces between quarks in spectra and enable tests of flavor-independent interactions.
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