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Extension of WKB-Topological Recursion Connection

  • Author / Creator
    Chotai, Anand W
  • It has been proven in other sources that spectral curves, $(\Sigma,x,y)$, where $\Sigma$ is a compact Riemann surface, and meromophic functions $x$ and $y$ satisfy a polynomial equation (and subject to certain admissibility conditions), can be used with the topological recursion to construct the WKB expansion for the quantization of said curve. In this paper we prove an extension of that connection for spectral curves, $(\Sigma,u,y)$, where $u$ is meromorphic only on an open region of $\Sigma$, and $x=e^u$ may or may not be meromorphic on $\Sigma$, so long as $y du$ is meromorphic on $\Sigma$; we will see that the admissibility condition still holds, and that there are added constraints. We provide a rigorous proof for dealing with spectral curves where $u$ is meromorphic on $\Sigma$, but provide only a conceptual argument and affirmative examples for dealing with spectral curves where $u$ is not meromorphic on $\Sigma$.

  • Subjects / Keywords
  • Graduation date
    2016-06:Fall 2016
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3MW28K7G
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematical Physics
  • Supervisor / co-supervisor and their department(s)
    • Bouchard, Vincent (Mathematics and Statistical Sciences)
  • Examining committee members and their departments
    • Bouchard, Vincent (Mathematics and Statistical Sciences)
    • Gannon, Terry (Mathematics and Statistical Sciences)
    • Patnaik, Manish (Mathematics and Statistical Sciences)
    • Favero, David (Mathematics and Statistical Sciences)