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- Discussion Type
- discussion topicequivariant localization
- Category Latest Changes
- Started by zskoda
- Comments 3
- Last comment by Urs
- Last Active Oct 28th 2020

equivariant localization (only good references and links for now) and Michael Atiyah

- Discussion Type
- discussion topicepimorphism
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by John Baez
- Last Active Oct 28th 2020

felt like adding a handful of basic properties to epimorphism

- Discussion Type
- discussion topicVasily Pestun
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 28th 2020

brief

`category: people`

-entry for hyperlinking references at*equivariant de Rham cohomology*

- Discussion Type
- discussion topicAdS-CFT
- Category Latest Changes
- Started by Urs
- Comments 16
- Last comment by Urs
- Last Active Oct 28th 2020

- Discussion Type
- discussion topicKaluza-Klein monopole
- Category Latest Changes
- Started by Urs
- Comments 5
- Last comment by Urs
- Last Active Oct 27th 2020

I have tried to clarify a bit more at

*Kaluza-Klein monopole*, and at*D6-brane*

- Discussion Type
- discussion topicKK-monopole geometries -- table
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 27th 2020

- Discussion Type
- discussion topicmesoscopic physics
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 27th 2020

- Discussion Type
- discussion topicmicrometer
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 27th 2020

- Discussion Type
- discussion topicnanometer
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 27th 2020

- Discussion Type
- discussion topicsupersymmetry
- Category Latest Changes
- Started by Urs
- Comments 46
- Last comment by Urs
- Last Active Oct 27th 2020

I’ll be working a bit on supersymmetry.

Zoran, you had once left two query boxes there with complaints. The second one is after this bit of the original entry (this will change any minute now)

The theory of supergravity is, as a classical field theory, an action functional on functions on a supermanifold $X$ which is invariant under the super-diffeomorphism group of $X$.

where you say

Zoran: action functional is on paths, even paths in infinitedimensional space, but not on point-functions.

I think you got something mixed up here. If $X$ is spacetime, a field on $X$

*is*the “path” that you want to see. The statement as given is correct, but I’ll try to expand on it.The second complaint is after where the original entry said

many models that suggest that the familiar symmetry of various action functionals should be enhanced to a supersymmetry in order to more properly describe fundamental physics.

You wrote:

This is doubtful and speculative. There are many models which have supersymmetry which is useful in their theoretical analysis, but the same models can be treated in formalisms not knowing about supersymmetry. Wheather the fundamental physics needs a model which has nontrivial supersymmetry is a speculative statement, and I disagree with equating theoretical physics with one direction in “fundamental physics”. I do not understand how can a model suggest supersymmetry; it is rather experimental evidence or problems with nonsupersymmetric models. Also one should distinguish the supersymmetry at the level of Lagrangean and the supersymmetry which holds only for each solution of the equation of motion.

I’ll rephrase the original statement to something less optimistic, but i do think that supersymmetry is suggsted more by looking at the formal nature of models than by lookin at the nature of nature. If you have a gauge theory for some Lie algebra (gravity, Poincaré Lie algebra) and the super extension of the Lie algebra has an interesting classification theory (the super Poincar´ algebra) then it is more th formalist in us who tends to feel compelled to investigate this than the phenomenologist. Supersymmetry is studied so much because it looks compelling on paper. Not because we have compelling phenomenological evidence. On the contrary.

So, if you don’t mind, I will remove both your query boxes and slightly polish the entry. Let’s have any further discussion here.

- Discussion Type
- discussion topicSupersymmetries and their Representations
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 27th 2020

added these pointers:

For analogous discussion see

- Steven Shnider,
*The superconformal algebra in higher dimensions*, Letters in Mathematical Physics November 1988, Volume 16, Issue 4, pp 377-383 (doi:10.1007/BF00402046)

and for review see

- Shiraz Minwalla, Section 4.2 of:
*Restrictions imposed by superconformal invariance on quantum field theories*, Adv. Theor. Math. Phys. 2, 781 (1998) (arXiv:hep-th/9712074, doi:10.4310/ATMP.1998.v2.n4.a4)

- Steven Shnider,

- Discussion Type
- discussion topicsuperconformal symmetry -- table
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Oct 27th 2020

this table used to be hidden at

*supersymmetry*, but it really ought to cross-link its entries. Therefore here its stand-alone version, for !inclusion

- Discussion Type
- discussion topicM5-brane
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active Oct 27th 2020

I have added to

*M5-brane*a fairly detailed discussion of the issue with the fractional quadratic form on differential cohomology for the dual 7d-Chern-Simons theory action (from Witten (1996) with help of Hopkins-Singer (2005)).In the new section

*Conformal blocks and 7d Chern-Simons dual*.

- Discussion Type
- discussion topicAlbert Einstein
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 27th 2020

added this pointer:

Peter Coles,

*Einstein, Eddington, and the 1919 Eclipse*(arxIv:astro-ph/0102462)(on the experimental confirmation of general relativity)

- Discussion Type
- discussion topicSchwinger effect
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Oct 27th 2020

- Discussion Type
- discussion topicD=5 super Yang-Mills theory
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Oct 27th 2020

added pointer to more references, in particular these on the relation to the D=6 N=(2,0) SCFT via KK-compactification on a circle fiber, hence as worldvolume theory of the D4-brane double dimensional reduction of the M5-brane:

Nathan Seiberg, Sec. 7 of

*Notes on Theories with 16 Supercharges*, Nucl. Phys. Proc. Suppl. 67:158-171, 1998 (arXiv:hep-th/9705117){#Douglas11} Michael Douglas,

*On D=5 super Yang-Mills theory and (2,0) theory*, JHEP 1102:011, 2011 (arXiv:1012.2880)Neil Lambert, Constantinos Papageorgakis, Maximilian Schmidt-Sommerfeld,

*M5-Branes, D4-Branes and Quantum 5D super-Yang-Mills*, JHEP 1101:083, 2011 (arXiv:1012.2882){#Witten11} Edward Witten, Sections 4 and 5 of

*Fivebranes and Knots*(arXiv:1101.3216)Chris Hull, Neil Lambert,

*Emergent Time and the M5-Brane*, JHEP06(2014)016 (arXiv:1403.4532)Andreas Gustavsson,

*Five-dimensional Super-Yang-Mills and its Kaluza-Klein tower*. JHEP01(2019)222 (arXiv:1812.01897)Neil Lambert, Sec. 3.1 and 3.4.3. of

*Lessons from M2’s and Hopes for M5’s*,*Proceedings of the LMS-EPSRC Durham Symposium:**Higher Structures in M-Theory, August 2018*Fortschritte der Physik, 2019 (arXiv:1903.02825, slides pdf)

- Discussion Type
- discussion topicMax Zimet
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 27th 2020

- Discussion Type
- discussion topicArnav Tripathy
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 27th 2020

- Discussion Type
- discussion topicRiemannian orbifold
- Category Latest Changes
- Started by Urs
- Comments 19
- Last comment by Urs
- Last Active Oct 27th 2020

- Discussion Type
- discussion topicsimplicial loop space
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 26th 2020

added pointer to

- Danny Stevenson,
*Décalage and Kan’s simplicial loop group functor*, Theory and Applications of Categories, Vol. 26, 2012, No. 28, pp 768-787 (arXiv:1112.0474, tac:26-28)

- Danny Stevenson,

- Discussion Type
- discussion topicsimplicial object
- Category Latest Changes
- Started by Urs
- Comments 8
- Last comment by Urs
- Last Active Oct 26th 2020

added to simplicial object a section on the canonical simplicial enrichment and tensoring of $D^{\Delta^{op}}$ for $D$ having colimits and limits.

- Discussion Type
- discussion topicmodel structure on simplicial groups
- Category Latest Changes
- Started by Urs
- Comments 2
- Last comment by Urs
- Last Active Oct 26th 2020

added pointer to the original statement in

- Daniel Quillen, p. II 3.7 of:
*Axiomatic homotopy theory*in:*Homotopical Algebra*, Lecture Notes in Mathematics 43, Springer 1967(doi:10.1007/BFb0097438)

- Daniel Quillen, p. II 3.7 of:

- Discussion Type
- discussion topicderivator
- Category Latest Changes
- Started by Urs
- Comments 81
- Last comment by Mike Shulman
- Last Active Oct 26th 2020

Added to derivator the explanation that Denis-Charles Cisinski had posted to the blog.

Zoran, I have made the material you had here the section "References", as this was mainly pointers to the literature. Please move material that you think you should go into other sections.

- Discussion Type
- discussion topicBorel model structure
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 25th 2020

- Discussion Type
- discussion topicBN-pair
- Category Latest Changes
- Started by nLab edit announcer
- Comments 3
- Last comment by Urs
- Last Active Oct 25th 2020

- Discussion Type
- discussion topictensor triangulated category
- Category Latest Changes
- Started by Urs
- Comments 7
- Last comment by Urs
- Last Active Oct 24th 2020

In articles by Balmer I see “tensor monoidal category” to be explained as a triangulated category equipped with a symmetric monoidal structure such that tensor product with any object “is an exact functor”, but I don’t see where he is specific about what “exact functor” is meant to mean. Maybe I am just not looking in the right article.

Clearly one wants it to mean “preserving exact triangles” in some evident sense. One place where this is made precise is in def. A.2.1 (p.106) of Hovey-Palmieri-Strickland’s “Axiomatic stable homotopy theory” (pdf).

However, these authors do not use the terminology “tensor triangulated” but say “symmetric monoidal compatible with the triangulation”. On the other hand, Balmer cites them as a reference for “tensor triangulated categories” (e.g. page 2 of his “The spectrum of prime ideals in tensor triangulated categories” ).

My question is: may I assume that “tensor triangulated category” is used synonymously with Hovey-Palmieri-Strickland’s “symmetric monoidal comaptible with the triangulation”?

- Discussion Type
- discussion topicDrinfeld center
- Category Latest Changes
- Started by Urs
- Comments 6
- Last comment by Urs
- Last Active Oct 24th 2020

- Discussion Type
- discussion topicspectrum of a tensor triangulated category
- Category Latest Changes
- Started by Urs
- Comments 1
- Last comment by Urs
- Last Active Oct 24th 2020

added pointer to

Paul Balmer,

*The spectrum of prime ideals in tensor triangulated categories*. J. Reine Angew. Math., 588:149–168, 2005 (arXiv:math/0409360)Paul Balmer,

*Spectra, spectra, spectra—tensor triangular spectra versus Zariski spectra of endomorphism rings*, Algebr. Geom. Topol., 10(3):1521–1563, 2010 (pdf)

(which have been listed at

*Paul Balmer*all along, but were missing here, strangely)and to the recent:

- Kent B. Vashaw,
*Balmer spectra and Drinfeld centers*(arXiv:2010.11287)

- Discussion Type
- discussion topicmodel structure on equivariant dgc-algebras
- Category Latest Changes
- Started by Urs
- Comments 4
- Last comment by Urs
- Last Active Oct 24th 2020

starting something, on

- Laura Scull,
*A model category structure for equivariant algebraic models*, Transactions of the American Mathematical Society 360 (5), 2505-2525, 2008 (doi:10.1090/S0002-9947-07-04421-2)

- Laura Scull,

- Discussion Type
- discussion topicKlein four-group
- Category Latest Changes
- Started by Urs
- Comments 3
- Last comment by Urs
- Last Active Oct 24th 2020