000206559 001__ 206559 000206559 005__ 20211110130209.0 000206559 0247_ $$2arXiv$$aarXiv:1410.3382 000206559 0247_ $$2altmetric$$aaltmetric:2770950 000206559 0247_ $$2inspire$$ainspire:1321735 000206559 037__ $$aPUBDB-2015-01023 000206559 0881_ $$aDESY-14-181; arXiv:1410.3382 000206559 088__ $$2DESY$$aDESY-14-181 000206559 088__ $$2arXiv$$aarXiv:1410.3382 000206559 1001_ $$aGrassi, Alba$$b0$$eCorresponding Author 000206559 245__ $$aTopological Strings from Quantum Mechanics 000206559 260__ $$c2014 000206559 3367_ $$2DRIVER$$apreprint 000206559 3367_ $$028$$2EndNote$$aElectronic Article 000206559 3367_ $$0PUB:(DE-HGF)25$$2PUB:(DE-HGF)$$aPreprint$$bpreprint$$mpreprint$$s1448872163_24197 000206559 3367_ $$2BibTeX$$aARTICLE 000206559 3367_ $$0PUB:(DE-HGF)15$$2PUB:(DE-HGF)$$aInternal Report$$mintrep 000206559 500__ $$aOA 000206559 520__ $$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 P2, local P1xP1 and local F1. 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, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry. 000206559 536__ $$0G:(DE-HGF)POF2-514$$a514 - Theoretical Particle Physics (POF2-514)$$cPOF2-514$$fPOF II$$x0 000206559 536__ $$0G:(EU-Grant)317089$$aGATIS - Gauge Theory as an Integrable System (317089)$$c317089$$fFP7-PEOPLE-2012-ITN$$x1 000206559 588__ $$aDataset connected to arXivarXiv 000206559 650_7 $$2INSPIRE$$astring: topological 000206559 650_7 $$2INSPIRE$$aspace: Calabi-Yau 000206559 650_7 $$2INSPIRE$$astring model: topological 000206559 650_7 $$2INSPIRE$$aoperator: spectrum 000206559 650_7 $$2INSPIRE$$acorrection: nonperturbative 000206559 650_7 $$2INSPIRE$$aspectral 000206559 650_7 $$2INSPIRE$$aquantum mechanics 000206559 650_7 $$2INSPIRE$$aquantization 000206559 650_7 $$2INSPIRE$$adeterminant 000206559 650_7 $$2INSPIRE$$amembrane model 000206559 650_7 $$2INSPIRE$$aFermi gas 000206559 650_7 $$2INSPIRE$$aorbifold 000206559 693__ $$0EXP:(DE-MLZ)NOSPEC-20140101$$5EXP:(DE-MLZ)NOSPEC-20140101$$eNo specific instrument$$x0 000206559 7001_ $$0P:(DE-H253)PIP1018306$$aHatsuda, Yasuyuki$$b1$$udesy 000206559 7001_ $$aMarino, Marcos$$b2 000206559 8564_ $$uhttps://bib-pubdb1.desy.de/record/206559/files/1410.3382v2.pdf$$yOpenAccess 000206559 8564_ $$uhttps://bib-pubdb1.desy.de/record/206559/files/1410.3382v2.gif?subformat=icon$$xicon$$yOpenAccess 000206559 8564_ $$uhttps://bib-pubdb1.desy.de/record/206559/files/1410.3382v2.jpg?subformat=icon-1440$$xicon-1440$$yOpenAccess 000206559 8564_ $$uhttps://bib-pubdb1.desy.de/record/206559/files/1410.3382v2.jpg?subformat=icon-180$$xicon-180$$yOpenAccess 000206559 8564_ $$uhttps://bib-pubdb1.desy.de/record/206559/files/1410.3382v2.jpg?subformat=icon-640$$xicon-640$$yOpenAccess 000206559 8564_ $$uhttps://bib-pubdb1.desy.de/record/206559/files/1410.3382v2.jpg?subformat=icon-700$$xicon-700$$yOpenAccess 000206559 8564_ $$uhttps://bib-pubdb1.desy.de/record/206559/files/1410.3382v2.pdf?subformat=pdfa$$xpdfa$$yOpenAccess 000206559 909CO $$ooai:bib-pubdb1.desy.de:206559$$pdnbdelivery$$pec_fundedresources$$pVDB$$pdriver$$popen_access$$popenaire 000206559 9101_ $$0I:(DE-588b)2008985-5$$6P:(DE-H253)PIP1018306$$aDeutsches Elektronen-Synchrotron$$b1$$kDESY 000206559 9132_ $$0G:(DE-HGF)POF3-611$$1G:(DE-HGF)POF3-610$$2G:(DE-HGF)POF3-600$$aDE-HGF$$bForschungsbereich Materie$$lMaterie und Universum$$vFundamental Particles and Forces $$x0 000206559 9131_ $$0G:(DE-HGF)POF2-514$$1G:(DE-HGF)POF2-510$$2G:(DE-HGF)POF2-500$$3G:(DE-HGF)POF2$$4G:(DE-HGF)POF$$aDE-HGF$$bStruktur der Materie$$lElementarteilchenphysik$$vTheoretical Particle Physics$$x0 000206559 9141_ $$y2014 000206559 915__ $$0StatID:(DE-HGF)0510$$2StatID$$aOpenAccess 000206559 915__ $$0StatID:(DE-HGF)0580$$2StatID$$aPublished 000206559 9201_ $$0I:(DE-H253)T-20120731$$kT$$lTheorie-Gruppe$$x0 000206559 980__ $$apreprint 000206559 980__ $$aVDB 000206559 980__ $$aintrep 000206559 980__ $$aI:(DE-H253)T-20120731 000206559 980__ $$aUNRESTRICTED 000206559 9801_ $$aFullTexts