OEQ examples Sample Clauses

OEQ examples. ‌ We have seen how to construct id-defects for any potential. This can be generalised to group orbifolds and symmetry defects. If the potential W is invariant under some finite W group action, x '→ g(x), g ∈ G, one can form defects Ig with non zero quantum dimen- W sions by replacing, the matrix factor Ji with Jg = xi − g(yi). The concept of orbifold equivalences has been extended beyond the ideal of group orb- ifolds, [24, 26] such as some of the previously mentioned ADE series pairs. Not only are the MFs for these models all well known, and also have been shown to support the correspondence between LG and minimal models, but they provided the best possibility for orbifold equivalence due to the form of the A-model potential, as we shall see. Some of these potentials have the same central charge, and furthermore the A and D models are known to be orbifold equivalent but the E models were not so. For convenience we list them together. WAn = xn+1 + z2 , WDd = xd—1 + xy2 , WE6 = x3 + y4 , WE7 = x3 + xy3 , WE8 = x3 + y5 . with d ≥ 4 and n ≥ 2. ∼ ∼ { } { } { } Whenever two of these potentials have the same central charge, they have been shown to be orbifold equivalent; the classes with more than one representative are {Ad—1, Dd/2+1} for even d not equal to 12, 18 or 30, and A11, D7, E6 , A17, D10, E7 and A29, D16, E8 . The A D orbifold equivalences are related to (simple current) orbifolds in the CFT con- text, but the A E orbifold equivalences do not arise from any group action and are examples of symmetries beyond groups [24, 26]. In order to form a picture of these special MFs we will now reproduce a concrete ex- ample of an equivalence [26]. We will denote variables from the left potential Uas xi, and variables from the right potential V as yi. 2 A11 ∼oeq E6 with A11 = x12 + x2 and E6 = y3 + y4, Q(x, y) = 0 E (4.19) where the rank 2 matrices E, J are defined by 1,1 E = y2 − x + 1 y (sx )2 + 2t + 1 (sx )6 8 1 t + 1 4 4 1 E = −y + y (sx ) + (sx )