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An Algebra Isomorphism for the Landau-Ginzburg Mirror Symmetry Conjecture

Landau-Ginzburg mirror symmetry takes place in the context of affine singularities in CN. Given such a singularity defined by a quasihomogeneous polynomial W and an appropriate group of symmetries G, one can construct the FJRW theory (see [3]). This construction fills the role of the A-model in a mirror symmetry proposal of Berglund and H ubsch [1]. The conjecture is that the A-model of W and G should match the B-model of a dual singularity and dual group (which we denote by WT and GT). The B-model construction is based on the Milnor ring, or local algebra, of the singularity. We verify this conjecture for a wide class of singularities on the level of Frobenius algebras, generalizing work of Krawitz [10]. We also review the relevant parts of the constructions.

Identiferoai:union.ndltd.org:BGMYU2/oai:scholarsarchive.byu.edu:etd-3792
Date07 July 2011
CreatorsJohnson, Jared Drew
PublisherBYU ScholarsArchive
Source SetsBrigham Young University
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceTheses and Dissertations
Rightshttp://lib.byu.edu/about/copyright/

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