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Matrix models and eigenfunctions from the Topological String/Spectral Theory correspondence

Defense Thèse de doctorat : Univ. Genève, 2019 - Sc. 5303 - 2019/01/26
Abstract The Topological String/Spectral Theory (TS/ST) correspondence was introduced as a sharp, non-perturbative relationship between topological strings on toric Calabi-Yau threefolds on one side, and the spectral theory of operators given by the quantized mirror curve on the other side. It predicts a non-trivial relationship between enumerative invariants of the toric Calabi-Yau threefold and spectral quantities of the corresponding operator. This work explores three consequences and extensions of the TS/ST correspondence. First, we show that the TS/ST correspondence implies a new realization of the topological string as convergent matrix models. Second, we propose an extension of the TS/ST correspondence involving the open sector of topological strings on the TS side and the eigenfunctions of the operator on the ST side. Third, we investigate how the TS/ST correspondence and its interpretation in terms of a non-interacting Fermi gas can help us defining a sensible notion of "quantum curve".
Keywords Topological stringMatrix modelsSpectral theoryNon-perturbative effects
URN: urn:nbn:ch:unige-1147430
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Research group Groupe Marino Beiras
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ZAKANY, Szabolcs. Matrix models and eigenfunctions from the Topological String/Spectral Theory correspondence. Université de Genève. Thèse, 2019. doi: 10.13097/archive-ouverte/unige:114743 https://archive-ouverte.unige.ch/unige:114743

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Deposited on : 2019-03-04

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