Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 059, 31 pages      arXiv:1812.06200      https://doi.org/10.3842/SIGMA.2020.059

Mirror Symmetry for Nonabelian Landau-Ginzburg Models

Nathan Priddis a, Joseph Ward b and Matthew M. Williams c
a) Brigham Young University, USA
b) University of Utah, USA
c) Colorado State University, USA

Received September 24, 2019, in final form June 12, 2020; Published online June 27, 2020

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.

Key words: mirror symmetry; Landau-Ginzburg models; Calabi-Yau; nonabelian.

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