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John Baez (Jul 15 2023 at 14:13):A long time ago I read about an attempt to understand quarks using what I'll call "defective" monoidal categories: things like monoidal categories where the associator doesn't obey the pentagon identity.
John Baez (Jul 15 2023 at 14:13):At the time I wasn't interested - mainly because we already have a good theory of quarks.
John Baez (Jul 15 2023 at 14:14):However, now that I'm writing about the history of monoidal categories, I'd be interested to see attempts, no matter how flawed, to do something interesting with defective monoidal categories.
John Baez (Jul 15 2023 at 14:15):And so far I'm not finding that paper I'd seen!
John Baez (Jul 15 2023 at 14:15):Does anyone know about anything like this?
Todd Trimble (Jul 31 2023 at 22:25):Any pictures you can show us of what you remember?
John Baez (Jul 31 2023 at 23:15):Sorry, not really. My memories are quite vague, but idea was roughly that instead of the usual idea that quarks are described via the tautologous representation of color on , they are described by an object in a "defective monoidal category" (my own term just now, meaning something like a monoidal category where the pentagon identity doesn't hold). Somehow this was supposed to explain confinement (the fact that we only see particles that transform in the trivial rep of , like mesons and hadrons). However, I don't think the details were worked out enough to be convincing to me, especially since the usual theory works great.
John Baez (Jul 31 2023 at 23:17):The folks involved wanted me to visit them and talk about this, but I refused. I don't think I should name them because I may have the details mixed up, and I haven't been able to find any such paper written by the people who I thought had this idea.
John Baez (Jul 31 2023 at 23:17):(Or any such paper at all, for that matter.)
John Baez (Jul 31 2023 at 23:45):This is just one of several, probably quite a few, nonstandard theories attempting to explain color and confinement.