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I have added to string theory a new section Critical strings and quantum anomalies.
Really I was beginning to work on a new entry twisted spin^c structure (not done yet) and then I found that a summary discussion along the above lines had been missing.
I have added a pointer to Witten’s latest foundational article to string theory.
That made me look over that entry again. I have now divided the Idea-section into two pieces “conceptually” and “phenomenologically” and added a little paragraph under Idea - phenomenologically … which still doesn’t do justice to anything but which now at least serves as ambient commentary for that link to “string theory critics” which keeps floating around in the entry.
I have added a pointer to Witten’s latest foundational article
Is there any indication that your framing of physics in terms of higher gauge theory, in particular in terms of cohesive homotopy, would be useful for an article such as this? I mean do you read it and think about what Witten’s trying to do in terms of the language you write about here?
So the point of that article is that it is good and useful to take supergeometry seriously when working with super Riemann surfaces and in particular to regard their moduli space consistently in supergeometry, too, instead of trying to decompose it into pieces in ordinary differential geometry, as people have been doing for decades now.
And of course this is a step towards a more truthfully topos-theoretic discussion of superstring perturbation theory, eventually, where we pass to the cohesive context of smooth super infinity-groupoids and then stay there, meaning: really work internally there, instead of going external and doing unnatural things like dropping back to ordinary differential geometry.
That said, the article (and its two predecessors in the last weeks) is of course full with technical detail that as such is part of the concrete particular of this specific model of cohesion, instead of abstract general cohesion.
Once I get a free minute we’ll be pushing smooth super-cohesion further, as many cohesive treasures are lying there, just to be picked up.
That said, the article (and its two predecessors in the last weeks) is of course full with technical detail that as such is part of the concrete particular of this specific model of cohesion, instead of abstract general cohesion.
Presumably what appears to be concrete particular may actually be instances of abstract general. Is there a term to distinguish a concrete realization of an abstract general from a brute concrete particular? E.g., some aspects of the monster group follow from merely being a group, while others are special to the group.
In other words, maybe it’s just that Witten is writing in the style of Track Mod, but much may follow from the abstract general.
I see what you mean. I’ll send a reply later. No time right now. Just a quick remark: a few minutes after announcing it I renamed that to Layer Mod. More later, sorry.
copied the new (more comprehensive and more polished) list of references from string theory FAQ to here
In the section “References – History” I have added these pointers:
John Schwarz, The Early Years of String Theory: A Personal Perspective (arXiv:0708.1917), published as Gravity, unification, and the superstring, in Filippo Colomo, Paolo Di Vecchia (eds.) The birth of string theory, Cambridge University Press, (2011) (doi:10.1017/CBO9780511977725.005)
(on the early history of string theory up to the “first superstring revoluton”, the construction of the Green-Schwarz-anomaly-free $SO(32)$ type I string theory and heterotic string)
John Schwarz, The Second Superstring Revolution, Colloquium-level lecture presented at the Sakharov Conference (Moscow, May 1996) (arXiv:hep-th/9607067)
(on the “second superstring revolution”: the realization of D-branes, dualities in string theory and M-theory)
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