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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 13 Pith papers
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Non-relativistic limits of $\mathcal N=4$ supersymmetric Yang-Mills theory and S-duality
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, est...
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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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The Nahm transform of multi-fractional instantons
A fractional SU(N) instanton of charge r/N, embedded with U(1) fluxes, has a Nahm dual that is an SU(Nhat) fractional instanton of charge r/Nhat, with Nhat = N q1 q3 - r q3 + q1.
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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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Search for NS 3-form Flux Induced Vacua for the Critical Non-Abelian Vortex String
NS 3-form flux on the conifold generates a potential for the baryonic modulus b whose only vacuum is a runaway to infinity, degenerating the conifold.
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Gravitational wave signatures from reheating in Chern-Simons running-vacuum cosmology
Scalaron-induced gravitational waves in Chern-Simons running-vacuum cosmology have a universal f^6 high-frequency scaling, distinguishable from the f^7 scaling of general relativity, and may be detectable by future ob...
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General Composite Non-Abelian Strings and Flag Manifold Sigma Models
The paper constructs BPS composite vortex strings whose worldsheet dynamics is a Flag manifold sigma model with couplings fixed by flux differences, and gives GLSM and NLSM formulations.
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Quantum-Ordering Ambiguities in Weak Chern-Simons 4D Gravity and Metastability of the Condensate-Induced Inflation
In a Chern-Simons gravity model, quantum-ordering-dependent imaginary parts of the gravitational anomaly condensate give inflation a finite lifetime and imply the string scale is about one tenth of the Planck mass.
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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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Anyons on M5-Probes of Seifert 3-Orbifolds via Flux Quantization
Choosing equivariant twistorial Cohomotopy as the flux quantization law on single M5-probes wrapped on a Z2-orbifold yields abelian anyonic quantum states on the orbifold fixed locus.
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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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