Quantum periods and spectra in dimer models and Calabi-Yau geometries

Huang, Min–xin; Sugimoto, Yuji; Wang, Xin

doi:10.1007/jhep09(2020)168

Cited by 5 publications

(5 citation statements)

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“…Certainly, it would be interesting to further generalize the results to more Calabi-Yau geometries and consider a bigger moduli space instead of the one-parameter space in this paper. In the case of local Calabi-Yau geometries with multiple A-periods, it is found that their quantum corrections are described by the same differential operators [10]. It seems that the general formalism here would need to be much improved to find all the TBA-like equations for the quantum periods of the different A-cycles of a Calabi-Yau geometry.…”

Section: Jhep01(2021)002mentioning

confidence: 93%

“…Like R k (κ), we can also split the generating functions of φ l 's into 3 parts as 10) whereφ k denotes the complex conjugate of φ k . From the definitions of the functions, it is straightforward to find the relations between φ j to ρ j [18].…”

Section: Jhep01(2021)002mentioning

confidence: 99%

“…[6,7]. These developments in quantum periods lead to exciting results such as the calculations of topological string free energy in the NS limit [8], quantum spectra [9,10], exact quantizations including non-perturbative effects [11,12]. The quantum mirror maps for a class of del Pezzo Calabi-Yau geometries with exceptional symmetry are recently studied in [13].…”

Section: Introductionmentioning

confidence: 99%

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Quantum periods and TBA-like equations for a class of Calabi-Yau geometries

Huang

2021

J. High Energ. Phys.

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We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to a large class of Calabi-Yau geometries described by three-term quantum operators. We give two methods to derive the TBA-like equations. One method uses only elementary functions while the other method uses Faddeev’s quantum dilogarithm function. The two approaches provide different realizations of TBA-like equations which are nevertheless related to the same quantum period.

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Section: Jhep01(2021)002mentioning

confidence: 93%

Section: Jhep01(2021)002mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum periods and TBA-like equations for a class of Calabi-Yau geometries

Huang

2021

J. High Energ. Phys.

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“…See [47,[81][82][83] for more details about the derivation of the quantum operators D 2j from quantum curves.…”

Section: Jhep08(2022)207mentioning

confidence: 99%

Topological strings and Wilson loops

Huang

Lee

Wang

2022

J. High Energ. Phys.

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We propose the refined topological string correspondence to the expectation values of half-BPS Wilson loop operators in 5d $$ \mathcal{N} $$ N = 1 gauge theory partition function on the Omega-deformed background $$ {\mathbb{R}}_{\upepsilon_{1,2}}^4 $$ ℝ ϵ 1 , 2 4 × S1. We provide the refined topological vertex method and the refined holomorphic anomaly equation method in the topological string theory, from which we have exact computations on the 5d Wilson loops partition functions in both A- and B-models. Finally, with the exact results we have in B-model, we recover the quantum periods of local ℙ1 × ℙ1 model and local ℙ2 model in the study of quantum geometry and we further give a refined generalization of A-period.

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“…In relation to the spectral problem mentioned above, computation of the quantum period integrals is also an interesting problem [1,2,23,24,25,39]. Even in genus one cases they are technical challenges in particular for the fully massive E 6 , E 7 , E 8 cases.…”

Section: The Quantum Curve For Ementioning

confidence: 99%

Quantum Representation of Affine Weyl Groups and Associated Quantum Curves

Moriyama

Yamada

2021

SIGMA

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We study a quantum (non-commutative) representation of the affine Weyl group mainly of type E(1) 8 , where the representation is given by birational actions on two variables x, y with q-commutation relations. Using the tau variables, we also construct quantum "fundamental" polynomials F (x, y) which completely control the Weyl group actions. The geometric properties of the polynomials F (x, y) for the commutative case is lifted distinctively in the quantum case to certain singularity structures as the q-difference operators. This property is further utilized as the characterization of the quantum polynomials F (x, y). As an application, the quantum curve associated with topological strings proposed recently by the first named author is rederived by the Weyl group symmetry. The cases of type D(1)5 , E

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Quantum periods and spectra in dimer models and Calabi-Yau geometries

Cited by 5 publications

References 50 publications

Quantum periods and TBA-like equations for a class of Calabi-Yau geometries

Quantum periods and TBA-like equations for a class of Calabi-Yau geometries

Topological strings and Wilson loops

Quantum Representation of Affine Weyl Groups and Associated Quantum Curves

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