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Title 
Exact solutions to quantum spectral curves by topological string theory 

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Published in  Journal of High Energy Physics. 2015, vol. 1510, p. 02594  
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Open Access  SCOAP3 

Abstract  We generalize the conjectured connection between quantum spectral problems and topological strings to many local almost del Pezzo surfaces with arbitrary mass parameters. The conjecture uses perturbative information of the topological string in the unrefined and the NekrasovShatashvili limit to solve nonperturbatively the quantum spectral problem. We consider the quantum spectral curves for the local almost del Pezzo surfaces of F 2 , F 1 , ℬ 2 $$ {\mathbb{F}}_2,{\mathbb{F}}_1,{\mathrm{\mathcal{B}}}_2 $$ and a mass deformation of the E 8 del Pezzo corresponding to different deformations of the threeterm operators O 1,1 , O 1,2 and O 2,3 . To check the conjecture, we compare the predictions for the spectrum of these operators with numerical results for the eigenvalues. We also compute the first few fermionic spectral traces from the conjectural spectral determinant, and we compare them to analytic and numerical results in spectral theory. In all these comparisons, we find that the conjecture is fully validated with high numerical precision. For local F 2 $$ {\mathbb{F}}_2 $$ we expand the spectral determinant around the orbifold point and find intriguing relations for Jacobi theta functions. We also give an explicit map between the geometries of F 0 $$ {\mathbb{F}}_0 $$ and F 2 $$ {\mathbb{F}}_2 $$ as well as a systematic way to derive the operators O m , n from toric geometries.  
Keywords  Nonperturbative Effects — Topological Strings — String Duality  
Identifiers  arXiv: 1506.09176  
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Citation (ISO format)  GU, Jie et al. Exact solutions to quantum spectral curves by topological string theory. In: Journal of High Energy Physics, 2015, vol. 1510, p. 02594. doi: 10.1007/JHEP10(2015)025 https://archiveouverte.unige.ch/unige:77275 