Advances in Theoretical and Mathematical Physics

Volume 21 (2017)

Number 1

Duality for toric Landau–Ginzburg models

Pages: 243 – 287



Patrick Clarke (Department of Mathematics, University of Pennsylvania, Philadelphia, Penn., U.S.A.)


We introduce a duality construction for toric Landau–Ginzburg models, applicable to complete intersections in toric varieties via the sigma model / Landau–Ginzburg model correspondence. This construction is shown to reconstruct those of Batyrev-Borisov, Berglund–Hübsch, Givental, and Hori–Vafa. It can be done in more general situations, and provides partial resolutions when the above constructions give a singular mirror. An extended example is given: the Landau–Ginzburg models dual to elliptic curves in $(\mathbb{P}^1)^2$.


Landau–Ginzburg, mirror symmetry, complete intersection, toric variety

2010 Mathematics Subject Classification

Primary 14J32. Secondary 14J81, 14M10, 14M25.

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Please note: This online paper was *corrected* on April 11, 2017.