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Pseudo-periodic map and classification of theories with eight supercharges
by Dan Xie
Submission summary
| Authors (as registered SciPost users): | Dan Xie |
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| Preprint Link: | scipost_202404_00007v1 (pdf) |
| Date submitted: | 2024-04-08 08:54 |
| Submitted by: | Xie, Dan |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
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| Approach: | Theoretical |
Abstract
The classification of local one parameter Coulomb branch solution of theories with eight supercharges is given by assuming that it is given by a genus g fiberation of Riemann surfaces. The crucial point is the fact that certain conjugacy class (so-called pseudo-periodic map of negative type) in mapping class group determines the topological type of the degeneration. The classification of conjugacy class has a simple combinatorial description. Each such conjugacy class gives rise to a dual graph and a 3d mirror quiver gauge theory can be derived, which is then used to identify the low energy theory (assuming generic deformation). Some global Seiberg-Witten geometries are given by using the topological data of the degeneration. The geometric setup unifies 4d N = 2 SCFTs (such as Tn theory and Argyres-Douglas theory), 5d N = 1 SCFTs, 6d (1, 0) SCFTs, 4d IR free theories, and 4d asymptotical free theories in a single combinatorial framework.