Advances in Theoretical and Mathematical Physics

Volume 19 (2015)

Number 5

$p$-adic Berglund–Hübsch duality

Pages: 1115 – 1139



Marco Aldi (Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, Va., U.S.A.)

Andrija Peruničić (Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada)


Berglund–Hübsch duality is an example of mirror symmetry between orbifold Landau–Ginzburg models. In this paper we study a D-module-theoretic variant of Borisov’s proof of Berglund–Hübsch duality. In the $p$-adic case, the D-module approach makes it possible to endow the orbifold chiral rings with the action of a non-trivial Frobenius endomorphism. Our main result is that the Frobenius endomorphism commutes with Berglund–Hübsch duality up to an explicit diagonal operator.

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