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I added this to the entry for Nima Arkani-Hamed.
Urs (or anyone else) do you know anything about Nima’s recent interest in category theory?
“six months ago, if you said the word category theory to me, I would have laughed in your face and said useless formal nonsense, and yet it’s somehow turned into something very important in my intellectual life in the last six months or so” (@ 44:05 in The End of Space-Time July 2022)
I don’t know anything concretely about what is being alluded to here, but from the preceding discussion one expects that one can rephrase these diagrams as string diagrams in a suitable monoidal category.
(A report here by somebody who attended related talks doesn’t know more details either.)
Not sure what more to say. Just noting that 20+ years ago, when the topological string was still en vogue, string theorists were all into derived categories (e.g arXiv:hep-th/0403166) and their Bridgeland stability conditions for modelling D-branes and mirror symmetry. This wasn’t considered “useless” then.
In this October 2023 talk, he says (around 27:30) that categories of quiver representations are what he has been working on for a counting problem in kinematic space:
Title: All-Loop Scattering as A Counting Problem
Abstract: I will describe a new understanding of scattering amplitudes based on fundamentally combinatorial ideas in the kinematic space of the scattering data. I first discuss a toy model, the simplest theory of colored scalar particles with cubic interactions, at all loop orders and to all orders in the topological ‘t Hooft expansion. I will present a novel formula for loop-integrated amplitudes, with no trace of the conventional sum over Feynman diagrams, but instead determined by a beautifully simple counting problem attached to any order of the topological expansion. A surprisingly simple shift of kinematic variables converts this apparent toy model into the realistic physics of pions and Yang-Mills theory. These results represent a significant step forward in the decade-long quest to formulate the fundamental physics of the real world in a new language, where the rules of spacetime and quantum mechanics, as reflected in the principles of locality and unitarity, are seen to emerge from deeper mathematical structures.
Thanks, I see.
There is a fairly detailed discussion of the relevant quivers in arXiv:2201.09176 (but no real discussion of their representations)
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