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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeAug 12th 2015

Yesterday I had added some rough bits and pieces and some references to ADE singularity, and cross-linked with relevant entries such as ADE classification and M-theory on G2-manifolds. But for the moment this remains a stub.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMar 31st 2018

Edit to: ADE singularity by Urs Schreiber at 2018-04-01 00:52:32 UTC.

hyperlinked pointer to textbook by Ibanez-Uranga

• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeApr 13th 2018

The link to the pdf in

• Martin Wijnholt, slides 6-10 of String compactification, PITP 2014 (pdf)

wasn’t working, but I found an article of that name uploaded on nLab. But this document is not in slides form. Is the material from the old slides 6-10 contained in this document?

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeApr 13th 2018

but I found

Please remind me of the url that you are referring to here.

• CommentRowNumber5.
• CommentAuthorDavid_Corfield
• CommentTimeApr 13th 2018

It used to point to

https://pitp2014.ias.edu/sites/pitp2014.ias.edu/files/PITP2014_P3_wijnholt.pdf

which doesn’t work.

https://ncatlab.org/nlab/files/WijnholtCompactification14.pdf

which is from that conference.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeApr 13th 2018
• (edited Apr 13th 2018)

Thanks. Unfortunately, I don’t see the graphics anymore in that other pdf by Wijnholt.

But this was suboptimal anyway. Meanwhile Hisham has produced the perfect graphics that should go into this entry. Once our article is out, remind me to upload a copy of that improved illustration here.

• CommentRowNumber7.
• CommentAuthorDavid_Corfield
• CommentTimeApr 13th 2018

And at Nonabelian gauge groups and chiral fermions at orbifold singularities there are the graphics and a reference to Part III of Wijnholt 14, for which the pdf works but not the slides.

• CommentRowNumber8.
• CommentAuthorDavid_Corfield
• CommentTimeApr 13th 2018
• (edited Apr 13th 2018)

But the slides can be found at the conference site, so I may as well change the URLs.

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeApr 13th 2018

Okay, thanks. Would be nice if you have the energy to fix it. But it’s not worth a lot of effort. In a short while I will provide a better graphics to replace that one.

• CommentRowNumber10.
• CommentAuthorDavid_Corfield
• CommentTimeApr 13th 2018

Ok, fixed on three pages.

• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeApr 15th 2018
• (edited Apr 15th 2018)

added a more official reference by Miles Reid: Reid 87

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeMay 6th 2018

added pointer to the two articles by Kronheimer here on ADE-singularities in terms opf hyper-Kaehler geometry

• CommentRowNumber13.
• CommentAuthorUrs
• CommentTimeMay 6th 2018
• (edited May 6th 2018)

Gave the statement that the resolution of an ADE-singularity is by spheres touching along the corresponding Dynking diagram its own little Properties-subsection. Added explicit pointer to where this was first proven: duVal 1934 I, p. 1-3 (453-455)).

Also added pointer to Kronheimers hyper-Kaehler version of the story.

• CommentRowNumber14.
• CommentAuthorUrs
• CommentTimeMay 8th 2018

added pointer to Lamotke 86, chapter IV

• CommentRowNumber15.
• CommentAuthorUrs
• CommentTimeMay 17th 2018

Replaced the previous graphics with a better one and added some more pointers to the string theoretic interpretation (here)

• CommentRowNumber16.
• CommentAuthorUrs
• CommentTimeSep 12th 2019

I have cleaned-up, expanded, cross-linked and sub-sub-sectioned the list of references on ADE-singularities in string theory: here

• CommentRowNumber17.
• CommentAuthorUrs
• CommentTimeMay 9th 2022

I have added one more subsection with references, concerning type II string/D-branes on A(DE)-type singularities:

Have taken the liberty of adding a self-reference at the end:

The observation that the worldsheet 2d CFT correspoding to a string probing (a D-brane on) an $A_{\kappa-1}$-type singularity $\mathbb{H}/_{C_{\kappa + 2}}$ is the chiral WZW model for the affine Lie algebra su(2) at level $\kappa - 2$ (plus some trivial summands):

On how this $\widehat{\mathfrak{su}(2)}^{\kappa-2}$-CFT encodes the BPS states of $SU(\kappa)$-SYM on D3-branes transverse to the singularity:

An interpretation of this phenomenon, under the expected K-theory classification of D-brane charge, as due to the (somewhat neglected) sector of twisted equivariant K-theory where the twist is by an inner local systems which may appear inside an A-type singularity: