From the Hitchin section to opers through nonabelian Hodge

DOI10.4310/jdg/1612975016zbMath1458.53035OpenAlexW3128324631WikidataQ115164534 ScholiaQ115164534MaRDI QIDQ2228091

Andrew Neitzke, Motohico Mulase, Olivia Dumitrescu, Georgios Kydonakis, Laura Fredrickson, Rafe R. Mazzeo

Publication date: 16 February 2021

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jdg/1612975016

zbMATH Keywords

moduli space of Higgs bundlesopersHitchin's equationsnonabelian Hodge correspondence

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) (14D21) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15)

Related Items (9)

Simpson-Mochizuki correspondence for \(\lambda\)-flat bundles ⋮ The Kapustin-Witten equations and nonabelian Hodge theory ⋮ Nilpotent Higgs bundles and families of flat connections ⋮ Parabolic opers and differential operators ⋮ Supersymmetric field theories and geometric Langlands: The other side of the coin ⋮ A journey from the Hitchin section to the oper moduli ⋮ Interplay between opers, quantum curves, WKB analysis, and Higgs bundles ⋮ Why is Landau-Ginzburg link cohomology equivalent to Khovanov homology? ⋮ Exact WKB and the quantum Seiberg-Witten curve for 4d \(N = 2\) pure SU(3) Yang-Mills. Abelianization

Cites Work

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• Erratum to: ``Darboux coordinates, Yang-Yang functional, and gauge theory
• Exact WKB analysis and cluster algebras
• The Self-Duality Equations on a Riemann Surface
• Constructing Variations of Hodge Structure Using Yang-Mills Theory and Applications to Uniformization

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