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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.
Edit to: ADE singularity by Urs Schreiber at 2018-04-01 00:52:32 UTC.
Author comments:
hyperlinked pointer to textbook by Ibanez-Uranga
The link to the pdf in
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?
but I found
Please remind me of the url that you are referring to here.
It used to point to
https://pitp2014.ias.edu/sites/pitp2014.ias.edu/files/PITP2014_P3_wijnholt.pdf
which doesn’t work.
You’ve uploaded
https://ncatlab.org/nlab/files/WijnholtCompactification14.pdf
which is from that conference.
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.
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.
But the slides can be found at the conference site, so I may as well change the URLs.
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.
Ok, fixed on three pages.
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.
added pointer to Lamotke 86, chapter IV
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):
Hirosi Ooguri Cumrun Vafa, p. 10-12 of: Two-Dimensional Black Hole and Singularities of CY Manifolds, Nucl. Phys. B 463 (1996) 55-72 (arXiv:hep-th/9511164, doi:10.1016/0550-3213%2896%2900008-9)
Wolfgang Lerche, Carsten Andrew Lütken, Christoph Schweigert, p. 4 of: D-Branes on ALE Spaces and the ADE Classification of Conformal Field Theories, Nucl.Phys. B 622 (2002) 269-278 (doi:10.1016/S0550-3213%2801%2900613-7, arXiv:hep-th/0006247)
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:
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