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@ARTICLE{Grassi:315831,
      author       = {Grassi, Alba and Hatsuda, Yasuyuki and Mariño, Marcos},
      title        = {{T}opological {S}trings from {Q}uantum {M}echanics},
      journal      = {Annales Henri Poincaré},
      volume       = {17},
      number       = {11},
      issn         = {1424-0661},
      address      = {Basel},
      publisher    = {Birkhäuser},
      reportid     = {PUBDB-2016-06100, DESY-14-181. arXiv:1410.3382},
      pages        = {3177 - 3235},
      year         = {2016},
      note         = {(c) Springer International Publishing},
      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 $\mathbb{P}^2$, 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.},
      cin          = {T},
      ddc          = {530},
      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)16},
      UT           = {WOS:000385208100007},
      eprint       = {1410.3382},
      howpublished = {arXiv:1410.3382},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:1410.3382;\%\%$},
      doi          = {10.1007/s00023-016-0479-4},
      url          = {https://bib-pubdb1.desy.de/record/315831},
}