Hitchin systems in N=2 field theory

Abstract

This is the second article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J. Teschner. The space of vacua of class $\mathcal{S}$ theories on $R^3\times S^1$ can be identified as the moduli space of solutions to the self-duality equations in two dimensions on Riemann surfaces studied by Hitchin. This fact plays a fundamental role for recent studies of the spectrum of BPS states in class $\mathcal{S}$ theories, and it is related to the integrable structure underlying Seiberg-Witten theory of theories of class $\mathcal{S}$. This article reviews important aspects of the role of the Hitchin system for the infrared physics of class $\mathcal{S}$ theories.

arXiv comment23 pages, see also overview article arXiv:1412.7145

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Cited by in corpus (6)

• A review of the T_N theory and its cousins
• A slow review of the AGT correspondence
• A geometric recipe for twisted superpotentials
• From $S^1$-fixed points to $\mathcal{W}$-algebra representations
• The (2,0) Superalgebra, Null M-branes and Hitchin's System
• Connecting Localization and Wall-Crossing via D-Branes