Timeline for Instanton Moduli Space on ALE Spaces
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 2, 2023 at 2:12 | comment | added | TaiatLyu | Sorry for inquiry after a long time, but why moduli of instantons of type(1, k) isomorphic to Hilbert scheme of k points? I know it’s true if underlying manifold is P^2, but I have no idea for general case. | |
| Mar 6, 2017 at 19:37 | comment | added | Benighted | So if I'm considering a generating function of something like elliptic genera of moduli space of $U(1)$ instantons on $A_{M-1}$, then I really have a gauge theory partition function on $A_{M-1}$ as opposed to $\mathbb{C}^{2}$? Like you say, this is where the ALE space is the spacetime itself. So I take it these crazy product formulas out there should relate Yang-Mills theory on $A_{M-1}$ spaces to topological string theories. | |
| Mar 6, 2017 at 11:21 | comment | added | user25309 | Yes, moduli space of $U(1)$ instantons of second Chern class $k$ on a ALE space (or any complex surface) is the same thing as the Hilbert scheme of $k$ points on this ALE space (or complex surface). | |
| Mar 5, 2017 at 20:46 | comment | added | Benighted | Couldn't have asked for better answer, thank you :) If I'm understanding correctly, $\mathcal{M}_{1}(k,N)$ are the instanton moduli spaces on $\mathbb{C}^{2}$, where for $N=1$, these are simply Hilbert schemes. Really the crux of what I've been wondering is this: letting $N=1$, is $\mathcal{M}_{M}(k,1)$ also simply the Hilbert scheme of $k$ point on the $A_{M-1}$ resolutions? Also, your physics explanation at the end is fantastic. Thanks a lot. I was definitely confused about the difference between putting these resolutions as internal manifolds vs. the spacetime itself. | |
| Mar 5, 2017 at 20:42 | vote | accept | Benighted | ||
| Mar 5, 2017 at 19:25 | history | answered | user25309 | CC BY-SA 3.0 |