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Opers and nonabelian Hodge: numerical studies

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arxiv 2007.00503 v3 pith:VDQASAFA submitted 2020-07-01 math.DG hep-th

Emily Dumas , Andrew Neitzke This is my paper
classification math.DGhep-th
keywords experimentshitchinconjecturehodgemetricnonabeliannumericalopers
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We present numerical experiments that test the predictions of a conjecture of Gaiotto-Moore-Neitzke and Gaiotto concerning the monodromy map for opers, the nonabelian Hodge correspondence, and the restriction of Hitchin's hyperk\"ahler metric to the Hitchin section. These experiments are conducted in the setting of polynomial holomorphic differentials on the complex plane, where the predictions take the form of conjectural formulas for the Stokes data and the Hitchin metric tensor. Overall, the results of our experiments support the conjecture.

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  1. Exact WKB of solutions by Borel summation and open TBA

    hep-th 2025-07 conditional novelty 7.0 of 10

    Borel-summed WKB solutions of quantum Seiberg-Witten equations are matched, numerically, to GMN open TBA solutions for the Weber and modified Mathieu equations.

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