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기하학수리물리연구단
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Mirror symmetry for exceptional unimodular singularities

Cited 3 time in webofscience Cited 5 time in scopus
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Title
Mirror symmetry for exceptional unimodular singularities
Author(s)
Changzheng Li; Li S.; Saito K.; Shen Y.
Subject
FJRW theory, ; Landau-Ginzburg model, ; Mirror symmetry, ; Primitive form, ; Singularity
Publication Date
2017-04
Journal
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, v.19, no.4, pp.1189 - 1229
Publisher
EUROPEAN MATHEMATICAL SOC
Abstract
In this paper, we prove the mirror symmetry conjecture between the Saito-Givental theory of exceptional unimodular singularities on the Landau-Ginzburg B-side and the Fan-Jarvis-Ruan-Witten theory of their mirror partners on the Landau-Ginzburg A-side. On the B-side, we develop a perturbative method to compute the genus-0 correlation functions associated to the primitive forms. This is applied to the exceptional unimodular singularities, and we show that the numerical invariants match the orbifold-Grothendieck-Riemann-Roch and WDVV calculations in FJRW theory on the A-side. The coincidence of the full data at all genera is established by reconstruction techniques. Our result establishes the first examples of LG-LG mirror symmetry for weighted homogeneous polynomials of central charge greater than one (i.e. which contain negative degree deformation parameters). © European Mathematical Society 2017
URI
https://pr.ibs.re.kr/handle/8788114/3429
DOI
10.4171/JEMS/691
ISSN
1435-9855
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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2017_CZL_Mirror symmetry for exceptional unimodular singularities.pdfDownload

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