Constructs a family of non-relativistic limits of 4d MSYM via brane setups that organize into a 3D moduli space with nontrivial topology where PSL(2,Z) dualities act more complexly than in the relativistic theory, establishing Abelian duality by path integral and supporting non-Abelian case via spec
TASI Lectures on Solitons
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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.
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Abelian instantons generated by dyon loops carry full instanton charge in the Georgi-Glashow model and form a continuous deformation of small BPST instantons.
The local moduli space of charge-r/N self-dual instantons on a twisted T^4 is identified with the Higgs branch of a 4d N=2 theory on intersecting D5-branes, reproducing prior field-theory results with manifest hyper-Kähler structure.
The hadron spectrum in N=2 SQCD with N_f=2N is given by the spectrum of a non-Abelian string on a 2D N=2 supersymmetric black hole, with a Higgs-to-string phase transition viewed as a conifold transition.
In an anisotropic holographic model of 3D QCD, hadronic systems become unstable when anisotropy exceeds the confinement energy scale, with dragging terms essential for transport properties.
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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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 charge-r/N self-dual instantons on a twisted T^4 is identified with the Higgs branch of a 4d N=2 theory on intersecting D5-branes, reproducing prior field-theory results with manifest hyper-Kähler structure.