Abstract
We have spent so many pages to study \(\mathcal{N}=2\) gauge theories with gauge group \(\mathop{\mathrm{SU}}(2)\). In this chapter we move on to the analysis of larger gauge groups.
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Notes
- 1.
This is not hard to derive. Let us say we triangulate the curve C with V vertices, E edges and F triangles so that the branch points are all at the vertices. We have \(\chi (C) = V - E + F\). We can just lift the edges and triangles to \(\Sigma \): we have NE edges and NF triangles. The vertices are however less than NV. At each vertex p i let the degree of the branching be degp i . Then there are \(\mathit{NV} -\sum (\deg p_{i} - 1)\) vertices in the triangulation of \(\Sigma \). We end up \(\chi (S) = N\chi (C) -\sum _{i}(\deg p_{i} - 1)\).
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Tachikawa, Y. (2015). Theories with Other Simple Gauge Groups. In: N=2 Supersymmetric Dynamics for Pedestrians. Lecture Notes in Physics, vol 890. Springer, Cham. https://doi.org/10.1007/978-3-319-08822-8_11
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