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.

29 pages

References in corpus (6)

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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
• 3-dimensional defect TQFTs and their tricategories
• 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
• Orbifold graph TQFTs
• Orbifold completion of 3-categories