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A (0,2) mirror map. (English) Zbl 1294.81223
Summary: We study the linear sigma model subspace of the moduli space of (0,2) super-conformal world-sheet theories obtained by deforming (2,2) theories based on Calabi-Yau hypersurfaces in reflexively plain toric varieties. We describe a set of algebraic coordinates on this subspace, formulate a (0,2) generalization of the monomial-divisor mirror map, and show that the map exchanges principal components of singular loci of the mirror half-twisted theories. In non-reflexively plain examples the proposed map yields a mirror isomorphism between subfamilies of linear sigma models.

MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81T60 Supersymmetric field theories in quantum mechanics 81T10 Model quantum field theories 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 14M25 Toric varieties, Newton polyhedra, Okounkov bodies 14J33 Mirror symmetry (algebro-geometric aspects)
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References:
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