Mirror Symmetry for open r-spin invariants

Mark Gross; Tyler L. Kelly; Ran J. Tessler

doi:10.4310/PAMQ.2024.v20.n2.a9

Mirror Symmetry for open r-spin invariants

Mark Gross, Tyler L. Kelly, Ran J. Tessler

Mathematics

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Abstract

We show that a generating function for open r-spin enumerative invariants produces a universal unfolding of the polynomial x^r. Further, the coordinates parametrizing this universal unfolding are flat coordinates on the Frobenius manifold associated to the Landau-Ginzburg model (ℂ, x^r) via Saito-Givental theory. This result provides evidence for the same phenomenon to occur in higher dimension, proven in the sequel [GKT22].

Original language	English
Pages (from-to)	1005–1024
Number of pages	20
Journal	Pure and Applied Mathematics Quarterly
Volume	20
Issue number	2
DOIs	https://doi.org/10.4310/PAMQ.2024.v20.n2.a9
Publication status	Published - 3 Apr 2024

Bibliographical note

Acknowledgments:
The authors would like to thank Alexander Buryak and Robert Maher for discussions relating to this work. The first author acknowledges support from the EPSRC under Grants EP/N03189X/1, a Royal Society Wolfson Research Merit Award, and the ERC Advanced Grant MSAG. The second author acknowledges that this paper is based upon work supported by the UKRI and EPSRC under fellowships MR/T01783X/1 and EP/N004922/2. The third author, incumbent of the Lillian and George Lyttle Career Development Chair, acknowledges support provided by the ISF grant No. 335/19 and by a research grant from the Center for New Scientists of Weizmann Institute. We thank the referee for their useful comments that have improved the paper.

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10.4310/PAMQ.2024.v20.n2.a9

GrossM2023Mirror
This is the Accepted Author Manuscript of an article accepted for publication in Pure and Applied Mathematics Quarterly: final published version will be available at: https://dx.doi.org/10.4310/PAMQ.2024.v20.n2.a9
Accepted author manuscript, 371 KBLicence: None: All rights reserved

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1 Active

Open Mirror Geometry for Landau-Ginzburg Models
Kelly, T.
Medical Research Council
1/11/20 → 31/10/24
Project: Research Councils
Bridging Frameworks via Mirror Symmetry
Kelly, T.
Engineering & Physical Science Research Council
1/09/18 → 31/08/19
Project: Research Councils

Cite this

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title = "Mirror Symmetry for open r-spin invariants",

abstract = "We show that a generating function for open r-spin enumerative invariants produces a universal unfolding of the polynomial xr. Further, the coordinates parametrizing this universal unfolding are flat coordinates on the Frobenius manifold associated to the Landau-Ginzburg model (ℂ, xr) via Saito-Givental theory. This result provides evidence for the same phenomenon to occur in higher dimension, proven in the sequel [GKT22]. ",

author = "Mark Gross and Kelly, {Tyler L.} and Tessler, {Ran J.}",

note = "Acknowledgments: The authors would like to thank Alexander Buryak and Robert Maher for discussions relating to this work. The first author acknowledges support from the EPSRC under Grants EP/N03189X/1, a Royal Society Wolfson Research Merit Award, and the ERC Advanced Grant MSAG. The second author acknowledges that this paper is based upon work supported by the UKRI and EPSRC under fellowships MR/T01783X/1 and EP/N004922/2. The third author, incumbent of the Lillian and George Lyttle Career Development Chair, acknowledges support provided by the ISF grant No. 335/19 and by a research grant from the Center for New Scientists of Weizmann Institute. We thank the referee for their useful comments that have improved the paper. ",

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N2 - We show that a generating function for open r-spin enumerative invariants produces a universal unfolding of the polynomial xr. Further, the coordinates parametrizing this universal unfolding are flat coordinates on the Frobenius manifold associated to the Landau-Ginzburg model (ℂ, xr) via Saito-Givental theory. This result provides evidence for the same phenomenon to occur in higher dimension, proven in the sequel [GKT22].

AB - We show that a generating function for open r-spin enumerative invariants produces a universal unfolding of the polynomial xr. Further, the coordinates parametrizing this universal unfolding are flat coordinates on the Frobenius manifold associated to the Landau-Ginzburg model (ℂ, xr) via Saito-Givental theory. This result provides evidence for the same phenomenon to occur in higher dimension, proven in the sequel [GKT22].

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Mirror Symmetry for open r-spin invariants

Abstract

Bibliographical note

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Projects

Open Mirror Geometry for Landau-Ginzburg Models

Bridging Frameworks via Mirror Symmetry

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