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@ARTICLE{Grassi:206559,
      author       = {Grassi, Alba and Hatsuda, Yasuyuki and Marino, Marcos},
      title        = {{T}opological {S}trings from {Q}uantum {M}echanics},
      reportid     = {PUBDB-2015-01023, DESY-14-181. arXiv:1410.3382},
      year         = {2014},
      note         = {OA},
      abstract     = {We 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.},
      keywords     = {string: topological (INSPIRE) / space: Calabi-Yau (INSPIRE)
                      / string model: topological (INSPIRE) / operator: spectrum
                      (INSPIRE) / correction: nonperturbative (INSPIRE) / spectral
                      (INSPIRE) / quantum mechanics (INSPIRE) / quantization
                      (INSPIRE) / determinant (INSPIRE) / membrane model (INSPIRE)
                      / Fermi gas (INSPIRE) / orbifold (INSPIRE)},
      cin          = {T},
      cid          = {I:(DE-H253)T-20120731},
      pnm          = {514 - Theoretical Particle Physics (POF2-514) / GATIS -
                      Gauge Theory as an Integrable System (317089)},
      pid          = {G:(DE-HGF)POF2-514 / G:(EU-Grant)317089},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)25 / PUB:(DE-HGF)15},
      eprint       = {1410.3382},
      howpublished = {arXiv:1410.3382},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:1410.3382;\%\%$},
      url          = {https://bib-pubdb1.desy.de/record/206559},
}