Operators and higher genus mirror curves

Codesido, Santiago; Gu, Jie; Mariño, Marcos

doi:10.1007/jhep02(2017)092

Cited by 37 publications

(60 citation statements)

References 117 publications

(363 reference statements)

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“…Fourthly, our analysis is directly applicable to other genus one matrix models [23,24], higher genus matrix models [21,48,49] or even matrix models of D type quiver [50,51]. Especially, in [23,24] the (2, 1, 2, 1) matrix model was studied and it was found to correspond to the E 7 spectral theory.…”

Section: Resultsmentioning

confidence: 87%

Hanany-Witten transition in quantum curves

Kubo

Moriyama

2019

J. High Energ. Phys.

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It was known that the U(N ) 4 super Chern-Simons matrix model describing the worldvolume theory of D3-branes with two NS5-branes and two (1, k)5-branes in IIB brane configuration (dual to M2-branes after taking the T-duality and the M-theory lift) corresponds to the D 5 quantum curve. For deformations of these two objects, on one hand the super Chern-Simons matrix model has three degrees of freedom (of relative rank deformations interpreted as fractional branes in brane configurations), while on the other hand the D 5 curve has five degrees of freedom (characterized by point configurations of asymptotic values). To identify the three-dimensional parameter space of brane configurations in the five-dimensional space of point configurations, we propose the necessity to cut the compact T-duality circle (or the circular quiver diagram) open, which is similar to the idea of "fixing a reference frame" or "fixing a local chart". Since the parameter space of curves enjoys the D 5 Weyl group beautifully, we are naturally led to conjecture that M2-branes are not only deformed by fractional branes but more obscure geometrical backgrounds.

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Section: Resultsmentioning

confidence: 87%

Hanany-Witten transition in quantum curves

Kubo

Moriyama

2019

J. High Energ. Phys.

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“…Based upon earlier constructions [19][20][21][22][23][24][25][26][27][28][29][30], it was proposed in [31] that there is a precise correspondence between the spectral theory of operators obtained by quantizing the mirror curve, and topological string theory on the toric Calabi-Yau geometry. This proposal has since led to many recent developments, e.g., [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51] (see [52] for an introduction). In addition, the topological string/spectral theory correspondence of [31] provides a nonperturbative definition of the topological-string partition function on toric Calabi-Yau geometries.…”

Section: Introductionmentioning

confidence: 99%

Resurgence matches quantization

Couso-Santamaría¹,

Mariño²,

Schiappa³

2017

J. Phys. A: Math. Theor.

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Abstract:The quest to find a nonperturbative formulation of topological string theory has recently seen two unrelated developments. On the one hand, via quantization of the mirror curve associated to a toric Calabi-Yau background, it has been possible to give a nonperturbative definition of the topological-string partition function. On the other hand, using techniques of resurgence and transseries, it has been possible to extend the string (asymptotic) perturbative expansion into a transseries involving nonperturbative instanton sectors. Within the specific example of the local P 2 toric Calabi-Yau threefold, the present work shows how the Borel-Padé-Ecalle resummation of this resurgent transseries, alongside occurrence of Stokes phenomenon, matches the string-theoretic partition function obtained via quantization of the mirror curve. This match is highly non-trivial, given the unrelated nature of both nonperturbative frameworks, signaling at the existence of a consistent underlying structure.

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“…We expect to have a similar situation for the operator (2.31) when ξ F 2 < −2. There are two indications that this is in fact what happens, as discussed in [4]. The first one is that, in some cases, the spectral traces of the operators (2.30), (2.31) can be computed in closed form as functions of ξ F 0 or ξ F 2 .…”

Section: Quantum Mirror Curvesmentioning

confidence: 81%

“…One can then use the topological string to obtain predictions for the spectral theory problem in the non-Hermitian case. One such prediction, already noted in [4], is that we will have generically an infinite discrete spectrum of complex eigenvalues, which can be easily computed on the string theory side by analytic continuation. The analysis of [4] focused on real values of the parameters leading to resonances.…”

Section: Introductionmentioning

confidence: 87%

“…One such prediction, already noted in [4], is that we will have generically an infinite discrete spectrum of complex eigenvalues, which can be easily computed on the string theory side by analytic continuation. The analysis of [4] focused on real values of the parameters leading to resonances. However, the predictions from topological string theory were not verified on the spectral theory side 1 .…”

Section: Introductionmentioning

confidence: 87%

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Resonances and PT symmetry in quantum curves

Emery

Mariño

Ronzani

2020

J. High Energ. Phys.

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In the correspondence between spectral problems and topological strings, it is natural to consider complex values for the string theory moduli. In the spectral theory side, this corresponds to non-Hermitian quantum curves with complex spectra and resonances, and in some cases, to PT-symmetric spectral problems. The correspondence leads to precise predictions about the spectral properties of these non-Hermitian operators. In this paper we develop techniques to compute the complex spectra of these quantum curves, providing in this way precision tests of these predictions. In addition, we analyze quantum Seiberg-Witten curves with PT symmetry, which provide interesting and exactly solvable examples of spontaneous PT-symmetry breaking.

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Operators and higher genus mirror curves

Cited by 37 publications

References 117 publications

Hanany-Witten transition in quantum curves

Hanany-Witten transition in quantum curves

Resurgence matches quantization

Resonances and PT symmetry in quantum curves

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