Abstract
AbstractSeiberg–Witten theory is a geometric framework to describe the low energy effective theory of \(\mathcal {N} = 2\) supersymmetric gauge theory in four dimensions [58, 59]. This geometric point of view gives rise to various interesting insights on gauge theory, including dualities in gauge theory, the brane dynamics in string/M-theory, connections with integrable system, etc. In this Chapter, we start with description of the low energy behavior of 4d \(\mathcal {N} = 2\) gauge theory, and discuss the geometric analysis based on Seiberg–Witten theory. We will then discuss its generalization to quiver gauge theory and supergroup gauge theory, and address the string/M-theory perspective with the brane description. We will also discuss the generalization to 5d \(\mathcal {N} = 1\) theory compactified on a circle, and 6d \(\mathcal {N} = (1,0)\) theory compactified on a torus.
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