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The BPS spectra of gauge theories in two and four dimensions

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TLDR
In this article, the exact BPS spectrum of these models is shown to coincide with the spectrum of massive hypermultiplets of certain = 2 supersymmetric abelian gauge theories in four dimensions.
Abstract
We study = (2,2) supersymmetric abelian gauge theories in two dimensions. The exact BPS spectrum of these models is shown to coincide with the spectrum of massive hypermultiplets of certain = 2 supersymmetric gauge theories in four dimensions. A special case of these results involves a surprising connection between four-dimensional = 2 SQCD with N colours and N$>Nf>N flavours at the root of the baryonic Higgs branch and the supersymmetric CP2N−Nf−1 σ-model in two dimensions. This correspondence implies a new prediction for the strong-coupling spectrum of the four-dimensional theory.

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Vortices, instantons and branes

TL;DR: In this article, the moduli space of vortices and instantons in non-commutative Yang-Mills-Higgs theories has been studied and a D-brane construction is presented in which the dynamics of Vortices is described by the Higgs branch of a gauge theory with 4 supercharges.
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Four-dimensional wall-crossing via three-dimensional field theory

TL;DR: In this article, the authors give a physical explanation of the Kontsevich-Soibelman wall-crossing formula for the BPS spectrum in Seiberg-Witten theories.
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Four-dimensional wall-crossing via three-dimensional field theory

TL;DR: In this paper, a physical explanation of the Kontsevich-Soibelman wall-crossing formula for the BPS spectrum in Seiberg-Witten theories is given.
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Generalised T-duality and non-geometric backgrounds

TL;DR: In this article, a generalised T-duality transition function is proposed for non-geometric backgrounds in string field theory, which are readily formulated in terms of a doubled geometry, related to generalised geometry.
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Vortex strings and four-dimensional gauge dynamics

TL;DR: In this paper, the low-energy quantum dynamics of vortex strings in the Higgs phase of = 2 supersymmetric QCD were studied, and the exact BPS spectrum of the stretched string was shown to coincide with the bimodal spectrum of four-dimensional parent gauge theory, which provided a physical explanation for an observation by Dorey relating the quantum spectra of theories in two and four dimensions.
References
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Journal ArticleDOI

Phases of N = 2 theories in two dimensions

TL;DR: In this paper, a natural relation between sigma models based on Calabi-Yau hypersurfaces in weighted projective spaces and Landau-Ginzburg models is found.
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Solutions of four-dimensional field theories via m-theory

TL;DR: In this paper, the Coulomb branch of a large family of four-dimensional N = 2 field theories with zero or negative beta function is studied, and explicit solutions for Coulomb branches are given.
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There are no Goldstone bosons in two-dimensions

TL;DR: In this article, it was shown that in two dimensions the Goldstone phenomenon can not occur; Goldstone's theorem does not end with two alternatives (either manifest symmetry or Goldstone bosons) but with only one (manifest symmetry).
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Fivebranes, membranes and non-perturbative string theory

TL;DR: In this article, nonperturbative instanton corrections to the moduli space geometry of type IIA string theory compactified on a Calabi-Yau space are derived and found to contain order e − 1/g s contributions, where g s is the string coupling.
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Supersymmetry algebras that include topological charges

TL;DR: In this paper, it was shown that the usual supersymmetric algebra is not valid for supersymmymmetric theories with solitons, and the algebra is modified to include the topological quantum numbers as central charges.
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