Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-02-01
JHEP 1107:068,2011
Physics
High Energy Physics
High Energy Physics - Theory
53 pages including 50 figures, v2: revised mainly for clarification with no change in main results; figures added, corrected a
Scientific paper
10.1007/JHEP07(2011)068
When the Seiberg-Witten curve of a four-dimensional $\mathcal{N}=2$ supersymmetric gauge theory wraps a Riemann surface as a multi-sheeted cover, a topological constraint requires that in general the curve should develop ramification points. We show that, while some of the branch points of the covering map can be identified with the punctures that appear in the work of Gaiotto, the ramification points give us additional branch points whose locations on the Riemann surface can have dependence not only on gauge coupling parameters but on Coulomb branch parameters and mass parameters of the theory. We describe how these branch points can help us to understand interesting physics in various limits of the parameters, including Argyres-Seiberg duality and Argyres-Douglas fixed points.
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