Orbifold equivalent potentials

Abstract

To a graded finite-rank matrix factorisation of the difference of two homogeneous potentials one can assign two numbers, the left and right quantum dimension. The existence of such a matrix factorisation with non-zero quantum dimensions defines an equivalence relation between potentials, giving rise to non-obvious equivalences of categories. Restricted to ADE singularities, the resulting equivalence classes of potentials are those of type {A_{d-1}} for d odd, {A_{d-1},D_{d/2+1}} for d even but not in {12,18,30}, and {A_{11}, D_7, E_6}, {A_{17}, D_{10}, E_7} and {A_{29}, D_{16}, E_8}. This is the result expected from two-dimensional rational conformal field theory, and it directly leads to new descriptions of and relations between the associated (derived) categories of matrix factorisations and Dynkin quiver representations.

arXiv comment29 pages

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Cited by in corpus (16)

• Notes on generalized global symmetries in QFT
• Orbifolds of n-dimensional defect TQFTs
• Discrete torsion defects
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• Lecture notes on 2-dimensional defect TQFT
• Decomposition, Trivially-Acting Symmetries, and Topological Operators
• Orbifolds of Reshetikhin-Turaev TQFTs
• Orbifolds by 2-groups and decomposition
• Realizing IR theories by projections in the UV
• Extending Landau-Ginzburg models to the point
• Calabi-Yau completions and orbifold equivalences
• Orbifold autoequivalent exceptional unimodal singularities
• On the Landau-Ginzburg/conformal field theory correspondence
• Hochschild cohomology and orbifold Jacobian algebras associated to invertible polynomials
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• Orbifold completion of 3-categories