Operators and higher genus mirror curves

@article{Codesido2016OperatorsAH,
  title={Operators and higher genus mirror curves},
  author={Santiago Codesido and Jie Gu and Marcos Mari{\~n}o},
  journal={Journal of High Energy Physics},
  year={2016},
  volume={2017},
  pages={1-53}
}
A bstractWe perform further tests of the correspondence between spectral theory and topological strings, focusing on mirror curves of genus greater than one with nontrivial mass parameters. In particular, we analyze the geometry relevant to the SU(3) relativistic Toda lattice, and the resolved ℂ3/ℤ6$$ {\mathbb{C}}^{{}^3}/{\mathbb{Z}}_6 $$ orbifold. Furthermore, we give evidence that the correspondence holds for arbitrary values of the mass parameters, where the quantization problem leads to… 
BPS relations from spectral problems and blowup equations
Recently, an exact duality between topological string and the spectral theory of operators constructed from mirror curves to toric Calabi–Yau threefold has been proposed. At the same time, an exact
The complex side of the TS/ST correspondence
The TS/ST correspondence relates the spectral theory of certain quantum mechanical operators, to topological strings on toric Calabi-Yau threefolds. So far the correspondence has been formulated for
Matrix models for topological strings: exact results in the planar limit
We study the large N expansion of a family of matrix models related to topological strings on toric Calabi-Yau threefolds. These matrix models compute spectral observables of underlying operators
Quantum curves and q-deformed Painlevé equations
We propose that the grand canonical topological string partition functions satisfy finite-difference equations in the closed string moduli. In the case of genus one mirror curve, these are
Quantized mirror curves and resummed WKB
A bstractBased on previous insights, we present an ansatz to obtain quantization conditions and eigenfunctions for a family of difference equations which arise from quantized mirror curves in the
A geometric approach to non-perturbative quantum mechanics
This work explores the connection between spectral theory and topological strings. A concrete example (the Y(3,0) geometry) of a conjectured exact relation between both based on mirror symmetry
Spectral theory and mirror symmetry
  • M. Mariño
  • Mathematics
    Proceedings of Symposia in Pure Mathematics
  • 2018
Recent developments in string theory have revealed a surprising connection between spectral theory and local mirror symmetry: it has been found that the quantization of mirror curves to toric
Calabi-Yau geometry and electrons on 2d lattices
The B-model approach of topological string theory leads to difference equations by quantizing algebraic mirror curves. It is known that these quantum mechanical systems are solved by the refined
Exact eigenfunctions and the open topological string
Mirror curves to toric Calabi-Yau threefolds can be quantized and lead to trace class operators on the real line. The eigenvalues of these operators are encoded in the BPS invariants of the
Wavefunctions, integrability, and open strings
A bstractIt has been recently conjectured that the exact eigenfunctions of quantum mirror curves can be obtained by combining their WKB expansion with the open topological string wavefunction. In
...
1
2
3
4
...

References

SHOWING 1-10 OF 85 REFERENCES
BPS relations from spectral problems and blowup equations
Recently, an exact duality between topological string and the spectral theory of operators constructed from mirror curves to toric Calabi–Yau threefold has been proposed. At the same time, an exact
Exact Results for Topological Strings on Resolved Y p,q Singularities
We obtain exact results in α′ for open and closed A-model topological string amplitudes on a large class of toric Calabi-Yau threefolds by using their correspondence with five dimensional gauge
Spectral Theory and Mirror Curves of Higher Genus
Recently, a correspondence has been proposed between spectral theory and topological strings on toric Calabi–Yau manifolds. In this paper, we develop in detail this correspondence for mirror curves
Quantum geometry of refined topological strings
A bstractWe consider branes in refined topological strings. We argue that their wavefunctions satisfy a Schrödinger equation depending on multiple times and prove this in the case where the
Matrix Models from Operators and Topological Strings, 2
The quantization of mirror curves to toric Calabi–Yau threefolds leads to trace class operators, and it has been conjectured that the spectral properties of these operators provide a non-perturbative
Exact solutions to quantum spectral curves by topological string theory
A bstractWe 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
Operators from Mirror Curves and the Quantum Dilogarithm
Mirror manifolds to toric Calabi–Yau threefolds are encoded in algebraic curves. The quantization of these curves leads naturally to quantum-mechanical operators on the real line. We show that, for a
SU(N) Geometries and Topological String Amplitudes
It has been conjectured recently that the field theory limit of the topological string partition functions, including all higher genus contributions, for the family of CY3folds giving rise to N = 2
Matrix Models from Operators and Topological Strings
We propose a new family of matrix models whose 1/N expansion captures the all-genus topological string on toric Calabi–Yau threefolds. These matrix models are constructed from the trace class
Topological Strings and (Almost) Modular Forms
The B-model topological string theory on a Calabi-Yau threefold X has a symmetry group Γ, generated by monodromies of the periods of X. This acts on the topological string wave function in a natural
...
1
2
3
4
5
...