Timeline for Is there a common genesis for ADE classifications?
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
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| Aug 16, 2010 at 14:13 | history | edited | JME | CC BY-SA 2.5 |
Spelling corrected
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| Aug 15, 2010 at 21:02 | history | edited | JME | CC BY-SA 2.5 |
Small precision
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| Aug 15, 2010 at 20:56 | comment | added | JME | @Paul, For the non-stringy part, you can read chapter 7 of Joyce's book "Compact Manifolds with Special Holonomy". This covers Kroheimer results on ALE. For the Yang-Mills instanton, I think it is best to just read his paper with Nakajima. Douglas and Moore's paper is also very well written but maybe a bit long. | |
| Aug 15, 2010 at 20:44 | history | edited | JME | CC BY-SA 2.5 |
Improved formating, small modifications, update following comments by Victor Protsak
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| Aug 11, 2010 at 17:33 | vote | accept | Paul Siegel | ||
| Aug 7, 2010 at 22:58 | comment | added | Paul Siegel | This is great - thanks! If I wanted to read more, would you recommend going directly to Douglas, Moore, Kronheimer, and Nakajima? Or are there better references? | |
| Aug 6, 2010 at 11:11 | comment | added | JME | Without D-branes there is no story at all connected the Kleinian singularities to the instanton moduli space. The tamed quiver is also a direct description of the D-brane picture. Finally, without D-branes there is also no reason to connect the Kleinian singularity to a 2 dimensional CFT. Why on earth a singularr 10 dimensional system will have a smooth 2 dimensional CFT description? It is an impressive aspect of the string description that the singular geometry is described by a smooth CFT. I have edited the text to make all these points clear. | |
| Aug 6, 2010 at 11:03 | history | edited | JME | CC BY-SA 2.5 |
Improved formatting and precision.
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| Aug 6, 2010 at 5:34 | comment | added | Victor Protsak | The reason I asked is because to me, at least, they are part of gauge theory, so I am not sure which part of your answer truly requires $D$-branes. | |
| Aug 6, 2010 at 2:00 | history | edited | JME | CC BY-SA 2.5 |
Corrected spelling
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| Aug 6, 2010 at 1:49 | comment | added | JME | The word "instanton" was invented by Gerard T'Hooft (a physicist) and the first examples of instantons on ALE were obtained by physicists as noticed in Kronheimer's original paper on ALE. Donaldson original paper is called "Application of gauge theory to 4 dimensional topology". However, I think that Donaldson invariants and instantons on ALE are part of mathematics in their own right. They get specially handy in string theory where they correspond to concrete physical concepts. | |
| Aug 6, 2010 at 0:37 | comment | added | Victor Protsak | This is mostly a terminological/context question: do you view Donaldson invariants and instantons on ALE spaces (as in the original work of Donaldson and Kronheimer) to be part of string theory? | |
| Aug 5, 2010 at 20:23 | history | answered | JME | CC BY-SA 2.5 |