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lkdvos
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lkdvos
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Overall looks amazing, thanks for getting this going!
I was wondering if there would be any way to document the checks we are performing, even if it is just with a math rendition of the actual equations that have to be fulfilled?
For example these could be attached to the @testsuite calls, simply to help future us understand what is going on.
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| # https://ncatlab.org/nlab/files/DelaneyModularTensorCategories.pdf#page=9 |
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That table seems extremely useful indeed.
src/sectors.jl
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| F2, F3 = Fsymbol(c, a, b, d, e, g), Fsymbol(a, b, c, d, g, f) | ||
| p2_o += F2 * R3 * F3 | ||
| if !symmetricbraiding | ||
| p2_u += F2 * conj(R3) * F3 |
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Shouldn't the R for the underbraiding be conj(Rsymbol(g, c, d)) instead of simply conjugating R3=Rsymbol(c, g, d) ?
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Yeah, that's indeed what you'd expect for general unitary braided fusion categories. I just checked and it turns out that all the braided categories in TKS are invariant under the order of a and b in Rsymbol(a, b, c). Interestingly, the ones that fail from CategoryData are the ones which fail the Artin braid test. This might hint at the Artin braids being done incorrectly.
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| # https://quantumkithub.github.io/TensorKit.jl/stable/man/sectors/#Manipulations-on-a-fusion-tree | ||
| @testsuite "Artin braid equality" I -> begin |
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I'm slightly confused by this additional check. It looks incredibly similar to the hexagon equation(s), up to some relabeling, and I assume it should just follow from the hexagon equations automatically?
Is this independent?
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I'm not sure how related much it actually is the hexagon equations, but indeed the braided coherence theorem says it should just follow from the hexagons. So it's not independent and maybe not worth checking? It does allow us to catch which sectors' braidings will be incompatible within TensorKit itself more quickly.
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Can you double check? I am writing this down and it seems like the two really do match up quite closely, but there are some conj differences, which makes me think that one of the options might actually contain a mistake for complex entries.
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Here I address #58, as well as check the two ways one can perform an Artin braid.
ZNElement{p}forp != 0has (temporarily) been set to not be braided, since these sectors definitely fail the additional tests. Surprisingly, it passes the hexagons, but fails already starting at the ribbon condition. I'm not too sure how to proceed with this, as it's apparently not easy to find a solution to the R-symbols which fulfills all the conditions.I tested SUNRepresentations up to
N = 5and CategoryData for these tests locally. Surprisingly, there are some braided categories in the latter which don't satisfy the Artin braid equality. The rest is fine.