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Mathematics > Algebraic Geometry

arXiv:1812.06200 (math)
[Submitted on 14 Dec 2018 (v1), last revised 29 Jun 2020 (this version, v4)]

Title:Mirror Symmetry for Nonabelian Landau-Ginzburg Models

Authors:Nathan Priddis, Joseph Ward, Matthew M. Williams
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Abstract:We consider Landau-Ginzburg models stemming from groups comprised of non-diagonal symmetries, and we describe a rule for the mirror LG model. In particular, we present the non-abelian dual group $G^\star$, which serves as the appropriate choice of group for the mirror LG model. We also describe an explicit mirror map between the A-model and the B-model state spaces for two examples. Further, we prove that this mirror map is an isomorphism between the untwisted broad sectors and the narrow diagonal sectors for Fermat type polynomials., we prove that this mirror map is an isomorphism between the untwisted broad sectors and the narrow diagonal sectors for Fermat type polynomials.
Comments: v3 fixes some errors in v2. Altogether 29 pages, 7 tables
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14N35, 53D37
Cite as: arXiv:1812.06200 [math.AG]
  (or arXiv:1812.06200v4 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1812.06200
Journal reference: SIGMA 16 (2020), 059, 31 pages
Related DOI: https://doi.org/10.3842/SIGMA.2020.059

Submission history

From: Nathan Priddis [view email]
[v1] Fri, 14 Dec 2018 23:04:08 UTC (18 KB)
[v2] Fri, 20 Sep 2019 23:01:21 UTC (28 KB)
[v3] Wed, 6 May 2020 19:17:42 UTC (31 KB)
[v4] Mon, 29 Jun 2020 22:22:52 UTC (33 KB)
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