In the item “Does string theory predict supersymmetry?”, after the paragraph saying that there is/was no theoretical reason for global $N=1$ compactifications, I have added the following line:

]]>However, recently arguments for a theoretical preference for $N=1$ supersymmetric compactifications have been advanced after all (FSS19, Sec. 3.4, Acharya 19).

All the more should I have cited it. But, to be frank, I had lost sight of its existence. You could have reminded me earlier. But it looks like the citation will make it to the final version now.

]]>Thanks! Anyway, the later sections were heavily dependent on your input.

]]>Oh, I see, sorry, good point. We haven’t sent back the galley proofs yet. I think. I’ll add in the citation now.

]]>I enjoyed the introductory chapter.

Section 3.2 might have earned me a second non-self citation for

- Duality as a category-theoretic concept, Studies in History and Philosophy of Modern Physics, Volume 59, August 2017, Pages 55-61, article.

But no. All I have so far is in A Schema for Duality, Illustrated by Bosonization:

]]>pure mathematicians sometimes work with uninterpreted theories; and duality is a grand theme in mathematics, just as it is in physics. But although comparing duality in mathematics and in physics would be a very worthwhile project, we set it aside. Cf. Corfield (2017)

while I was at it, I expanded the list of references (here), including items for all the textbooks that have their own nLab entries. Should have done this ages ago.

]]>did some minor edits in the item on supersymmetry. Then I added pointers to our Durham reviews to the item on nPOV in string theory (here)

]]>Interesting! Not sure I’d ever noticed that subsection Higher groupoid convolution algebras.

Roll on spring-time.

]]>I have a vague idea: Much NCG is secretly higher geometry. For instance most of the C*-algebras considered in Connes-style NCG are groupoid convolution algebras.

Moreover, the Wick algebras of free quantum fields are Moyal star-product algebras. But finite dimensional such are again (polarized) groupoid convolution algebras, namely of the symplectic groupoid (here).

Now the QFT Wick algebras are not finite dimensionaL BUT the relevant infinite-dimensional symplectic structure arises via transgression from the finite-dimensional but higher Poisson bracket on the jet bundle (seee the chapters “Symmetries” and “Observables” in the A first idea..). My hunch is that we may do (higher) groupoid convolution of the (higher) symplectic groupoid up on the jet bundle to get a finite-dimensional non-commutative algebra there and then somehow transgress that down to spacetime to the non-finite dimensional algebra of quantum observables.

This idea needs work. From spring on I will finally have time for research again… But right now I am sort of confident that this will work.

If this works out, then it would no longer be crazy to speculate that this works rather generally. But we have to see.

]]>Looking through some links from that answer, 2dCFT and 2-spectral triple, and on to your Physics Forums article, Spectral Standard Model and String Compactifications, got me wondering about the spectral approach. If the treatment in Modern Physics formalized in Modal Homotopy Type Theory and dcct looks to the geometric side of the algebra-geometry duality, is it that one can mimic all this dually in the algebraic operator approach?

Should there be a native logic for the algebraic operator approach, or are we just too wedded to the spatial?

Bit of a vague thought, but it is a Friday afternoon.

]]>Thanks!

The “which is in” just needs to be removed. I have fixed it now, also at *perturbative string theory vacuum*.

I wrote this in a bit of a haste, when somebody asked while I was really occupied with something else. Will try to come back to this. Possibly when finalizing chapter “15. Scattering” of the QFT series.

]]>I fixed the first two now, but don’t know what the last is supposed to say.

]]>I was looking to correct typos, but when submitting got told the page is locked and that I’m editing.

Anyway, at some point we need to change

$\mathbf{\Phi}^a(x) \Phi^b(y)$; theoris

and I’m not sure what is being said here:

]]>

in the given statethat the fields are in, which is in, which is defined thereby

I have added a further item

and made that also the Idea-section of a stub entry *perturbative string theory vacuum*.

This deserves to be polished and expanded more. But not tonight.

]]>Thanks!

Fixed the pointer now. It was trying to point to Erler-Gross at *causality*, but I had a superflous hash sign in there, which confused the parser.

I corrected a presumed spelling Grross –> Gross, but it looks like you intended Erler-Gross to be a bibliographic reference which is not yet under References.

]]>prompted by public demand (on PO here) I have added another item to the string theory FAQ:

But I don’t really have time for this at the moment, so I left it brief, with mainly a quote from the literature doing the job.

]]>I have expanded the item *What are the equations of string theory?*, prompted by the question coming up again on PF, here.

Doesn’t vev deserve a page of its own?

It does deserve a page of its own, yes.

]]>I was hinting that something needed to be added but only if there’s the energy. Doesn’t vev deserve a page of its own?

]]>We wouldn’t want those compact dimensions to rip open.

Interestingly, Penroses’ claim (in section 10.3 here) is the opposite: in gravity field theory his singularity theorem generically implies that small compact dimensions quickly collapse to a singularity.

I see room that the arguments in the string theory literature for that this does not happen due to stringy flux fields and non-perturbative effects may be imperfect. But I suppose if so, then it is these arguments that would need discussion, and not a different argument in field theoretic gravity. The instability of Kaluza-Klein-compactifications in field theoretic gravity was of course the reason why KK-theory was abandoned back in the beginning of the 20th century.

Does the relevant potential still allow fluctuations around a value?

Sure, it’s just a potential well.

Thanks for the cross-links with vev-s!

]]>That’s reassuring. We wouldn’t want those compact dimensions to rip open.

Does the relevant potential still allow fluctuations around a value?

By the way, I put in a link on moduli stabilization to vacuum expectation value. The latter redirects to a stub for condensate.

]]>Prompted by people wondering about remarks in Roger Penrose’s new book on the (lack of) stability of 4d spacetime in the presence of a KK-compactification (e.g. on PhysicsForums here), I have added to the string theory FAQ an item *Do the extra dimensions lead to instability of 4 dimensional spacetime?*.

That slide 29 – man, he needs to read some Edward Tufte … and make references for these grand claims

Every item on that slide is reviewing published material. The references are all listed, one by one, in section 7 of the article:

moduli stabilization: arXiv:0701034

gravitino masses: arXiv:1408.1961

heavy scalars: arXiv:0801.0478

suppressed gaugino masses arXiv:/0606262

solution to hierarchy problem: arXiv:0701034

non-thermal cosmology: arXiv:0804.0863

baryogenesis arXiv:1108.5178

axion stabilization arXiv:1004.5138

Higgs mass: arXiv:1211.2231 (that reference is indeed missing in section 7)

electric dipole moments arXiv:1405.7719

gluino predictions arXiv:1408.1961