000315831 001__ 315831 000315831 005__ 20250730111442.0 000315831 0247_ $$2doi$$a10.1007/s00023-016-0479-4 000315831 0247_ $$2ISSN$$a1424-0637 000315831 0247_ $$2ISSN$$a1424-0661 000315831 0247_ $$2WOS$$aWOS:000385208100007 000315831 0247_ $$2datacite_doi$$a10.3204/PUBDB-2016-06100 000315831 0247_ $$2inspire$$ainspire:1321735 000315831 0247_ $$2arXiv$$aarXiv:1410.3382 000315831 0247_ $$2openalex$$aopenalex:W1911154180 000315831 037__ $$aPUBDB-2016-06100 000315831 041__ $$aEnglish 000315831 082__ $$a530 000315831 088__ $$2DESY$$aDESY-14-181 000315831 088__ $$2arXiv$$aarXiv:1410.3382 000315831 0881_ $$aDESY-14-181 000315831 1001_ $$0P:(DE-HGF)0$$aGrassi, Alba$$b0$$eCorresponding author 000315831 245__ $$aTopological Strings from Quantum Mechanics 000315831 260__ $$aBasel$$bBirkhäuser$$c2016 000315831 3367_ $$2DRIVER$$aarticle 000315831 3367_ $$2DataCite$$aOutput Types/Journal article 000315831 3367_ $$0PUB:(DE-HGF)16$$2PUB:(DE-HGF)$$aJournal Article$$bjournal$$mjournal$$s1598001848_3207 000315831 3367_ $$2BibTeX$$aARTICLE 000315831 3367_ $$2ORCID$$aJOURNAL_ARTICLE 000315831 3367_ $$00$$2EndNote$$aJournal Article 000315831 500__ $$a(c) Springer International Publishing 000315831 520__ $$aWe propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi–Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized theta function. The perturbative part of this quantization condition is given by the Nekrasov–Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local $\mathbb{P}^2$, local $\mathbb{P}^{1} × \mathbb{P}^1$ and local $\mathbb{F}_1$. In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators. Physically, our results provide a non-perturbative formulation of topological strings on toric Calabi–Yau manifolds, in which the genus expansion emerges as a ’t Hooft limit of the spectral traces. Since the spectral determinant is an entire function on moduli space, it leads to a background-independent formulation of the theory. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry. 000315831 536__ $$0G:(DE-HGF)POF2-514$$a514 - Theoretical Particle Physics (POF2-514)$$cPOF2-514$$fPOF II$$x0 000315831 536__ $$0G:(EU-Grant)317089$$aGATIS - Gauge Theory as an Integrable System (317089)$$c317089$$fFP7-PEOPLE-2012-ITN$$x1 000315831 588__ $$aDataset connected to CrossRef 000315831 693__ $$0EXP:(DE-MLZ)NOSPEC-20140101$$5EXP:(DE-MLZ)NOSPEC-20140101$$eNo specific instrument$$x0 000315831 7001_ $$0P:(DE-H253)PIP1018306$$aHatsuda, Yasuyuki$$b1 000315831 7001_ $$aMariño, Marcos$$b2 000315831 773__ $$0PERI:(DE-600)2019605-2$$a10.1007/s00023-016-0479-4$$gVol. 17, no. 11, p. 3177 - 3235$$n11$$p3177 - 3235$$tAnnales Henri Poincaré$$v17$$x1424-0661$$y2016 000315831 7870_ $$0PUBDB-2015-01023$$aGrassi, Alba et.al.$$d2014$$iIsParent$$rDESY-14-181 ; arXiv:1410.3382$$tTopological Strings from Quantum Mechanics 000315831 8564_ $$uhttps://bib-pubdb1.desy.de/record/315831/files/1410.3382v3.pdf$$yPublished on 2016-04-09. 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