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Orbifold equivalent potentials | | Nils Carqueville
; Ana Ros Camacho
; Ingo Runkel
; | | Date: |
14 Nov 2013 | | 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. | | Source: | arXiv, 1311.3354 | | Services: | Forum | Review | PDF | Favorites | |
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