Strebel Differentials With Integral Lengths And Argyres-Douglas Singularities

Abstract

Strebel differentials are a special class of quadratic differentials with several applications in string theory. In this note we show that finding Strebel differentials with integral lengths is equivalent to finding generalized Argyres-Douglas singularities in the Coulomb moduli space of a U(N) $\mathbb{N}=2$ gauge theory with massive flavours. Using this relation, we find an efficient technique to solve the problem of factorizing the Seiberg-Witten curve at the Argyres-Douglas singularity. We also comment upon a relation between more general Seiberg-Witten curves and Belyi maps.

41 pages, 7 figures

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• Superconformal R-charges and dyon multiplicities in N=2 gauge theories
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• Multi-trace Correlators from Permutations as Moduli Space
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