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Permanent link (DOI): https://doi.org/10.7939/R3MW28K7G

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Extension of WKB-Topological Recursion Connection Open Access

Descriptions

Other title
Subject/Keyword
Topological Recursion
WKB
Mirror Symmetry
Hurwitz Numbers
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Chotai, Anand W
Supervisor and department
Bouchard, Vincent (Mathematics and Statistical Sciences)
Examining committee member and department
Patnaik, Manish (Mathematics and Statistical Sciences)
Gannon, Terry (Mathematics and Statistical Sciences)
Favero, David (Mathematics and Statistical Sciences)
Bouchard, Vincent (Mathematics and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematical Physics
Date accepted
2016-09-23T09:32:28Z
Graduation date
2016-06:Fall 2016
Degree
Master of Science
Degree level
Master's
Abstract
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 $\Sigma$.
Language
English
DOI
doi:10.7939/R3MW28K7G
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. 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.
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