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Reading the blog entry
and the reactions to it made me realize that apparently there is no comprehensive list either in print or online of all the insights into QFT in general and observed standard model physics in particular, that have been obtained via results in string theory.
So I have entertained myself with starting to collect notes for such a list:
In the process I have created a bunch of new entries, most of them stubs, linked to from there.
Added the famous Hadamard quote to the Idea-section of string theory results applied elsewhere:
Le plus court chemin entre deux vérités dans le domaine réel passe par le domaine complexe.
Thanks to Igor Khavkine for remining me of this quote in this context!
If you have another minute left, you could usefull add pointers also to the following:
string orientation of tmf (this was directly motivated from the index of the heterotic string (“Witten genus”))
the recent claims by Huang-Stoica-Yau on relation to Bruhat-Tits buldings and zeros of the Riemann zeta function (not sure yet if this will have implications on results, but it sure seems a noteworthy new mathematical perspective on zeta zeros.)
mirror symmetry (took complex geometers by complete surprise, but is easily seen from the 2d (2,0)-sigma model with target space the respective CY manifolds)
There is much more (for instance Morse theory of loop spaces via loop space supersymmetric quantum mechanics describing superstring propagatioon.) But I need to look into something else at the moment…
or Maryam Mirzakhani’s new proof of the Witten conjecture (which Witten, of course, was able to conjecture only due to insights from string theory)
speaking of Kontsevich (who first proved the Witten conjecture): of course also his proof of existence of deformation quantizations of all finite dimensional Poisson manifolds went through string theory (quantization appears as boundary theory of PSM topological string. The PSM string, in turn, Kontsevich had introduced as a unification of the A-model and the B-model topological string, in order to better understand mirror symetry)
OK, have added what you just wrote in #4. I wasn’t expecting a quick fix to the entry.
Looking on as an outsider, I was just experiencing the irrationality of the situation that Gregory Moore regrets that the formulation of M-theory “is a problem the community seems to have put aside - temporarily”. It’s inevitably going to tie up so many juicy pieces of mathematics already known to relate to aspects of string theory.
What you have in #5 and #6 are in the Fields medal section of string theory, linked to from here. I guess that section could be imported here. Probably all this deserves a page of its own.
Perhaps a project for another day.
added pointer to
of which today there is a review in
added pointer to
Added a quote by Michael Douglas
string theory “knows more mathematics than we do” and its study has led to the development of a large quantity of new mathematics: mirror symmetry (enumerative formulas, homological mirror symmetry, Bridgeland stability), new invariants (Gromov-Witten, Donaldson-Thomas, Gopakumar-Vafa, etc.), topological field theory and topological quantum gravity, etc.
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