GAUGE THEORY AND WILD RAMIFICATION

DOI10.1142/S0219530508001195zbMath1177.81101arXiv0710.0631OpenAlexW2158851808MaRDI QIDQ5503494

Edward Witten

Publication date: 15 January 2009

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.0631

zbMATH Keywords

isomonodromy deformationgeometric LanglandsStokes phenomena\(S\)-dualityHitchin equationsurface operator

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Topological field theories in quantum mechanics (81T45) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Algebraic number theory: global fields (11R99) Low-dimensional topology of special (e.g., branched) coverings (57M12) Ramification problems in algebraic geometry (14E22)

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Cites Work

• Unnamed Item
• Stable bundles and integrable systems
• Birkhoff invariants and Stokes' multipliers for meromorphic linear differential equations
• Jacobiennes des courbes spectrales et systèmes hamiltoniens complètement intégrables. (The Jacobians of spectral curves and completely integrable Hamiltonian systems)
• Geometry of the string equations
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• Harmonic metrics and connections with irregular singularities
• Construction of the moduli space of stable parabolic Higgs bundles on a Riemann surface
• Geometrical aspects of Schlesinger's equation
• Topological reduction of \(4\)D SYM to \(2\)D\(\sigma\)-models
• Mirror symmetry is \(T\)-duality
• Wild non-abelian Hodge theory on curves
• The Yang-Mills equations over Riemann surfaces
• Symplectic manifolds and isomonodromic deformations