# 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…

## 37 Citations

BPS relations from spectral problems and blowup equations

- MathematicsLetters in Mathematical Physics
- 2019

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

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2019

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

- Mathematics, Physics
- 2018

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

- MathematicsLetters in Mathematical Physics
- 2019

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

- MathematicsJournal of High Energy Physics
- 2019

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

- Mathematics
- 2018

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

- MathematicsProceedings 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

- Mathematics
- 2017

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

- Mathematics
- 2016

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

- MathematicsJournal of High Energy Physics
- 2019

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…

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