Seiberg-Witten Geometry of Four-Dimensional $\mathcal{N}=2$ Quiver Gauge Theories

Abstract

Seiberg-Witten geometry of mass deformed $\mathcal{N}=2$ superconformal ADE quiver gauge theories in four dimensions is determined. We solve the limit shape equations derived from the gauge theory and identify the space $\mathfrak{M}$ of vacua of the theory with the moduli space of the genus zero holomorphic (quasi)maps to the moduli space ${\mathrm{Bun}}_{\mathbf{G}}(\mathcal{E})$ of holomorphic $G^{\mathbb{C}}$-bundles on a (possibly degenerate) elliptic curve $\mathcal{E}$ defined in terms of the microscopic gauge couplings, for the corresponding simple ADE Lie group $G$. The integrable systems $\mathfrak{P}$ underlying the special geometry of $\mathfrak{M}$ are identified. The moduli spaces of framed $G$-instantons on ${\mathbb{R}}^2\times {\mathbb{T}}^2$, of $G$-monopoles with singularities on ${\mathbb{R}}^2\times {\mathbb{S}}^1$, the Hitchin systems on curves with punctures, as well as various spin chains play an important rôle in our story. We also comment on the higher-dimensional theories.

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Cited by in corpus (4)

• Higgs branch RG-flows via Decay and Fission
• di-Langlands correspondence and extended observables
• Massive vector field perturbations in the Schwarzschild spacetime from supersymmetric gauge theory
• Les Houches lectures on non-perturbative Seiberg-Witten geometry