TY  - EJOUR
AU  - Grassi, Alba
AU  - Hatsuda, Yasuyuki
AU  - Marino, Marcos
TI  - Topological Strings from Quantum Mechanics
IS  - DESY-14-181
M1  - PUBDB-2015-01023
M1  - DESY-14-181
M1  - arXiv:1410.3382
PY  - 2014
N1  - OA
AB  - 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.
KW  - string: topological (INSPIRE)
KW  - space: Calabi-Yau (INSPIRE)
KW  - string model: topological (INSPIRE)
KW  - operator: spectrum (INSPIRE)
KW  - correction: nonperturbative (INSPIRE)
KW  - spectral (INSPIRE)
KW  - quantum mechanics (INSPIRE)
KW  - quantization (INSPIRE)
KW  - determinant (INSPIRE)
KW  - membrane model (INSPIRE)
KW  - Fermi gas (INSPIRE)
KW  - orbifold (INSPIRE)
LB  - PUB:(DE-HGF)25 ; PUB:(DE-HGF)15
UR  - https://bib-pubdb1.desy.de/record/206559
ER  -