Lectures on the Topological Recursion for Higgs Bundles and Quantum Curves

DOI10.1142/9789813229099_0003zbMath1401.14001arXiv1509.09007OpenAlexW2125867128MaRDI QIDQ4556560

Motohico Mulase, Olivia Dumitrescu

Publication date: 16 November 2018

Published in: The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.09007

zbMATH Keywords

Higgs bundlestopological recursiontopological quantum field theoryquantum curvesHitchin spectral curves

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Topological field theories in quantum mechanics (81T45) Relationships between algebraic curves and integrable systems (14H70) Random matrices (algebraic aspects) (15B52) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry (14-01) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Classical hypergeometric functions, ({}_2F_1) (33C05) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Relationships between algebraic curves and physics (14H81) Families, moduli of curves (analytic) (14H15) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory (81-01) Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category (53D37) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items (9)

Painlevé 2 equation with arbitrary monodromy parameter, topological recursion and determinantal formulas ⋮ An invitation to 2D TQFT and quantization of Hitchin spectral curves ⋮ Generalized B-opers ⋮ Quantum curves from refined topological recursion: the genus 0 case ⋮ Holomorphic anomaly and quantum mechanics ⋮ A journey from the Hitchin section to the oper moduli ⋮ Singular vector structure of quantum curves ⋮ Quantum curves as quantum distributions ⋮ Interplay between opers, quantum curves, WKB analysis, and Higgs bundles

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