Quantum Hitchin Systems via β-Deformed Matrix Models View Full Text


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Article Info

DATE

2017-11-28

AUTHORS

Giulio Bonelli, Kazunobu Maruyoshi, Alessandro Tanzini

ABSTRACT

We study the quantization of Hitchin systems in terms of β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\beta}$$\end{document}-deformations of generalized matrix models related to conformal blocks of Liouville theory on punctured Riemann surfaces. We show that in a suitable limit, corresponding to the Nekrasov–Shatashvili one, the loop equations of the matrix model reproduce the Hamiltonians of the quantum Hitchin system on the sphere and the torus with marked points. The eigenvalues of these Hamiltonians are shown to be the ϵ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\epsilon_1}$$\end{document}-deformation of the chiral observables of the corresponding N=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal{N}=2}}$$\end{document} four dimensional gauge theory. Moreover, we find the exact wave-functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions. More... »

PAGES

1041-1064

References to SciGraph publications

  • 2012-04. Resolvents and Seiberg-Witten representation for a Gaussian β-ensemble in THEORETICAL AND MATHEMATICAL PHYSICS
  • 2011-09-05. Non-perturbative topological strings and conformal blocks in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-10-17. Quantization of integrable systems and a 2d/4d duality in JOURNAL OF HIGH ENERGY PHYSICS
  • 2012-06-29. Vertices, vortices & interacting surface operators in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-04-09. Nekrasov functions and exact Bohr-Sommerfeld integrals in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-02-05. Penner type matrix model and Seiberg-Witten theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 1996-02. Conformal blocks on elliptic curves and the Knizhnik-Zamolodchikov-Bernard equations in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2009-03-16. Topological expansion of the Bethe ansatz, and non-commutative algebraic geometry in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-05-19. Gauge theories on Ω-backgrounds from non commutative Seiberg-Witten curves in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-01-27. Loop and surface operators in gauge theory and Liouville modular geometry in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-01-12. Affine sl(N)conformal blocks from SU(N) gauge theories in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-01-11. Seiberg-Witten curve via generalized matrix model in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-07-11. Surface operator, bubbling Calabi-Yau and AGT relation in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-07-22. Seiberg-Witten theory, matrix model and AGT relation in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-09-27. The omega deformation, branes, integrability and Liouville theory in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-04-16. Matrix models for β-ensembles from Nekrasov partition functions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-09-12. Affine SL(2) Conformal Blocks from 4d Gauge Theories in LETTERS IN MATHEMATICAL PHYSICS
  • 2007-01-01. Seiberg-Witten Theory and Random Partitions in THE UNITY OF MATHEMATICS
  • 2012-08-06. N = 2 dualities in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-06-14. Classical conformal blocks from TBA for the elliptic Calogero-Moser system in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-07-12. Generalized matrix models and AGT correspondence at all genera in JOURNAL OF HIGH ENERGY PHYSICS
  • 2007-01-01. Lectures on the Langlands Program and Conformal Field Theory in FRONTIERS IN NUMBER THEORY, PHYSICS, AND GEOMETRY II
  • 2004-04-05. Matone's relation in the presence of gravitational couplings in JOURNAL OF HIGH ENERGY PHYSICS
  • 2006-01-10. 𝒩 = 1 superpotentials from multi-instanton calculus in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-07-01. Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2003-05-21. Multi-instanton calculus and equivariant cohomology in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-02-04. On AGT conjecture in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-01-22. Liouville Correlation Functions from Four-Dimensional Gauge Theories in LETTERS IN MATHEMATICAL PHYSICS
  • 2010-10-20. Relating gauge theories via Gauge/Bethe correspondence in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-10-05. Vortex Counting and Lagrangian 3-Manifolds in LETTERS IN MATHEMATICAL PHYSICS
  • 2004-10-19. Instantons on quivers and orientifolds in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-03-10. Genus-one correction to asymptotically free Seiberg-Witten prepotential from Dijkgraaf-Vafa matrix model in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-08-09. A& B model approaches to surface operators and Toda thoeries in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-09-08. A new 2d/4d duality via integrability in JOURNAL OF HIGH ENERGY PHYSICS
  • 2010-02-09. Matrix model conjecture for exact BS periods and Nekrasov functions in JOURNAL OF HIGH ENERGY PHYSICS
  • 2011-02. Topological expansion of the β-ensemble model and quantum algebraic geometry in the sectorwise approach in THEORETICAL AND MATHEMATICAL PHYSICS
  • 2011-04-07. Deforming SW curve in JOURNAL OF HIGH ENERGY PHYSICS
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    http://scigraph.springernature.com/pub.10.1007/s00220-017-3053-0

    DOI

    http://dx.doi.org/10.1007/s00220-017-3053-0

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1093058723


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