Thanks, I’ll fix that.

]]>topopological

Re #157

How about “…are what sources…”?

It’s a plural subject so should be

]]>

NS5-branesare what source…

Ideally the vanishing-at-infinity condition imposes a topological nontriviality condition, to make the solitonic branes stable against decaying away, as in the case of classical solitons. Does that happen here? I’m mindful of BPST instantons on 4d Euclidean space, where the decay condition/energy finiteness on the curvature make it extend to the sphere. But the connection itself is more like the singular/black brane case.

]]>I am expanding the section 4.1 to have more on the general idea of fundamental sigma-model branes in contrast to black/solitonic branes. Still telegraphic for the moment, but i added a diagram and a table which may be useful.

]]>That helps. Thanks!

]]>Right, I was about to add another paragraph on this.

There are (at least) *three* notions to be distinguished here, but terminology is inconsistent across authors:

singular/black branes: solutions of higher Einstein-Maxwell like equations where flux densities diverge at some singular locus

solitonic branes: solutions to higher Einstein-Maxwell equations where flux densities are finite everywhere but constrained to vanish at infinity,

sigma-model branes: objects propagating in a background of such fluxes.

For plain electromagnetism these three cases are

magnetic monopoles

Abrikosov vortices

electrons.

Now some authors say “solitonic brane” for “singular/black brane” and I was following this habit in the past, but it’s somewhat in tension with the original example of solitons (though there is no widely accepted definition of “soliton”, whence the ambiguity).

We should have an entry “solitonic brane” separate from “black brane”.

]]>topopological dyanmics

On p.5 “singular branes (black branes)” are contrasted with “solitonic branes”. Why at brane are fundamental $p$-branes contrasted with black $p$-branes (solitonic solutions)?

]]>Thanks, all fixed now.

Meanwhile I have been slowly progressing with fleshing out the first few pages of Section 4 “Resulting M5-brane sigma-model”…

]]>“its class in de Rham cohomology class” sounds odd

Typos:

]]>characted map; accomodates; eccept; the the Chern; tangntial; subtley

Yes, that works.

Another one: theit

]]>Thanks. How about “…are what sources…”?

]]>Great, I’m generally following so far.

Typos

duality-symemtric; euqations

and

]]>NS5-branes are that which sources – those which source

This Tuesday (June 27) at “Representations in higher structures” in Greifswald, I’ll be speaking about:

To go along with this we have been expanding the pdf notes-in-preparation.

Now there is some flesh on

- Section 1: “Branes imprinted on flux”

and

- Section 3: “Hypothesis H on M-Theory”

(The rest remains mostly telegraphic slide-show type material, for the time being.)

There is some ambition to make it accessible while keeping it brief. Comments are welcome.

]]>An article

- Fabio Apruzzi, Federico Bonetti, Iñaki García Etxebarria, Saghar S. Hosseini, Sakura Schafer-Nameki,
*Symmetry TFTs from String Theory*(arXiv:2112.02092)

referencing Twisted Cohomotopy implies M-theory anomaly cancellation on 8-manifolds

]]>More subtle questions require working on some generalised differential cohomology theory, of which there are many types. The generalised cohomology theory appropriate for M-theory has been postulated in [68]. It would be interesting to see if this more refined picture leads to any interesting consequences in field theory.

Ah, thanks, that was a bad oversight. Fixed now.

]]>This situation of twisted differential cohomology of curved spacetimes can of course be discussed, too (cite character article)

Missing citation

]]>Thanks, right. Fixed now. Have also improved the figure of the stereographic projection.

]]>Remark 2.2(a)

3-spheres $S^7$

2.2(e)

Finally, while flat Minkowski spacetimes themselves are homotopically trivial, it is this constraint that charges vanishing at infinity which makes them appear to their charge cohomology theory as effective spheres with non-trivial topology

is ungrammatical. ’Vanish’ rather than ’vanishing’?

to understand the n-sphere as being but the homeomorphism type…

’but’ in the sense of ’merely’ or ’simply’ sounds rather old-fashioned/poetic to my ear.

]]>A referee of “M/F-Theory as $M f$-theory” asked why there are no tangential twists considered in this article, even though the domains seem to be spheres. So we have now added some review and amplification of the nature of compactly supported charge cohomology on pages 6-8 of a revised pdf linked here.

]]>Thanks! Fixed now (here).

]]>]]>equivarint

Some typos in ’The character map in equivariant twistorial Cohomotopy’

]]>advencements; eqivariant (5 occasions)

Right, I agreed to give a 30 min “pre-talk”, which is what starts at 13:30. That’s why in total there will be $\sim$ 90 min.

]]>They have it advertised as 14-15 UK time on their site. But the Zoom session begins at 13.30, right?

I guess advertising is an internal affair.

]]>