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added these pointers
Discussion of quantum anomaly cancellation and 7d Horava-Witten theory is in
{#GherghettaKehagias02} Tony Gherghetta, Alex Kehagias, Anomaly Cancellation in Seven-Dimensional Supergravity with a Boundary, Phys.Rev. D68 (2003), 065019, (arXiv:hep-th/0212060)
Spyros D. Avramis, Alex Kehagias, _Gauged Supergravity on the Orbifold (arXiv:hep-th/0407221)
T.G. Pugh, Ergin Sezgin, Kellogg Stelle, / Heterotic Supergravity with Gauged R-Symmetry (arXiv:1008.0726)
Added pointer to today’s
Guillaume Bossard, Franz Ciceri, Gianluca Inverso, Axel Kleinschmidt, Maximal supergravities from higher dimensions [arXiv:2309.07232]
Guillaume Bossard, Franz Ciceri, Gianluca Inverso, Axel Kleinschmidt, Consistent truncation of eleven-dimensional supergravity on [arXiv:2309.07233]
I finally realized that this ought to exist. And sure enough, it had been constructed already: the 4d supergravity Lie 2-algebra-extension of the 4d super-Poincaré super-Lie algebra. I have added a minimum of an Idea-section and pointers to the references.
Minimal stub requested by links at reproducing kernel Hilbert space and few other entries.
a stub (though I did try my hand on a brief idea-section), for the moment mostly to provide a home for
stub for iterated integral (more references as soon as the nLab wakes up again…)
quick note for 5-dimensional Chern-Simons theory, for the moment just to record some references
added pointer to André Henriques’ recent MO comment here to quantization of 3d Chern-Simons theory. Should try to find time to work that into the entry.
gave 11d Chern-Simons theory its own (brief, for the moment) entry (splitting off some material from self-dual higher gauge theory)
Added a fair bit of content to 7d Chern-Simons theory.
Of the three examples discussed there, the first two are review. The third is inspired by something I have been talking about with D. Fiorenza, C. Rogers and H. Sati.
Changed title and links to different convention, see discussion here. (Unified redirects among articles about Chern-Simons theory in a particular dimension. There are now four for every artile “D=n Chern-Simons theories”, “nd Chern-Simons theory”, “nd Chern-Simons theories”, “n-dimensional Chern-Simons theory” and “n-dimensional Chern-Simons theories”.)
started adding these kinds of references, but maybe this should eventually go in its own stand-alone entry:
A kind of 4d Chern-Simons theory intermediated between ordinary 3d Chern-Simons theory and compled 3d (hence real 6d) holomorphic Chern-Simons theory:
Kevin Costello, Edward Witten, Masahito Yamazaki, Gauge Theory and Integrability, II, ICCM Not. 6, 120-146 (2018) (arXiv:1802.01579)
Kevin Costello, Edward Witten, Masahito Yamazaki, Gauge Theory and Integrability, I, ICCM Not. 6, 46-119 (2018) (arXiv:1709.09993)
Meer Ashwinkumar, Meng-Chwan Tan, Qin Zhao, Branes and Categorifying Integrable Lattice Models (arXiv:1806.02821)
Changed title and links to different convention, see discussion here. (Unified redirects among articles about Chern-Simons theory in a particular dimension. There are now four for every artile “D=n Chern-Simons theories”, “nd Chern-Simons theory”, “nd Chern-Simons theories”, “n-dimensional Chern-Simons theory” and “n-dimensional Chern-Simons theories”)
Changed title and links to different convention, see discussion here. (Unified redirects among articles about Chern-Simons theory in a particular dimension. There are now four for every artile “D=n Chern-Simons theories”, “nd Chern-Simons theory”, “nd Chern-Simons theories”, “n-dimensional Chern-Simons theory” and “n-dimensional Chern-Simons theories”)
Added to fix a dead link.
Discovering so called Magnus expansion, as an application of Lie theory to differential equations,
started M-theory on G2-manifolds
Used unicode subscripts for indices of exceptional Lie groups including title and links. When not linked, usual formulas are used. See discussion here. Links will be re-checked after all titles have been changed. (Removed two redirects for “G2-orbifold” from the top and added one for “G2-orbifold” at the bottom of the page.)
starting something (a bare list of references, to be !include
ed into relevant entries, such as at G2-manifold and conical singularity)
As a welcome means of procrastinating work on spectral sequence, I created G2-MSSM and touched or created stubs for a bunch of related entries, such as adding references to G2-manifold, creating model (in particle physics), disambiguating at model etc. pp.
added to E7 the statement of the decomposition of the smallest fundamental rep under and (here) and used this then to expand the existing paragraph on As U-duality group of 4d SuGra
added to G2 the definition of as the subgroup of that preserves the associative 3-form.
added statement of and references for some of the homotopy groups of to E8
expanded E6 a bit.
added some references on representationology of to F4
I’ve added to reflexive graph a definition of the free category of a reflexive quiver.
That page needs some reorganization because everything now said there is about reflective quivers, and not say about reflective undirected simple graphs.
Maybe free category also also needs touching up and maybe a link to reflective graph. I don’t know how to justify that the paths in the free category don’t contain identity edges.
Created 2-category with contravariance and 3-category with contravariance, combining ideas from this preprint of mine with ideas that Vladimir Sotirov had written at contravariant functor (which I moved from there to here).
There is a student here who is thinking about how to relate -algebraic theories with -operads and in the course of that also dendroidal sets with Lurie-type “-categories of operations” of -operads.
I am trying to help a bit where I can. First of all I thought I’d need to get a better idea of how the triangle
works in 1-category theory. So I am naturally looking at Mike’s Generalized Virtuology to get some hints.
I had planned to typeup the little that I understand about the relation between Lawvere theories and generalized multicategories, but now I ended up spending some time just on the entry on virtual double categories. Here is what I did
created a subsection “Monads on virtual double categories” with the basic definitions
and further subsections on “Monoids and modules” (this existed as an empty stub before)
and “Generalized multicategories” (with the basic definition, then pointing over to generalized multicategory of course).
I also
created vDbl
added the raw definition and the reference and virtual equipment.
I took the liberty of mentioning the term “fc-multicategory” at the beginning of virtual double category (because that happens to remind me easier of what the term refers to) and at virtual equipment I said that this term is short for “proarrow equipment of a virtual double category”.
(Hm, that summary of what i did is almost longer than the little bit of text that I acutally added! :-)
Mike, here is a question:
when I read your article with Cruttwell, I have slight trouble when it comes to definition 8.2 of normalized monoids. It has a horizontal morphism labeled where definition 4.2 has an equality. It seems. Is there a typo in one of these or did I miss some further definition in the intermediate four sections (not unlikely)?
Added a cross-reference to representable multicategory. It may be worth merging this page with that one.
Wrote a bit at double profunctor.
have added to (infinity,1)-operad the basics for the “-category of operators”-style definition
added to action groupoid a section on action oo-groupoids