Timeline for What is $SL(2,\mathbb{R})$-Chern-SImons Theory?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 4, 2019 at 17:32 | comment | added | Xenomorph | @Mtheorist Thank you for the link. I had read that paper. | |
| Apr 4, 2019 at 15:50 | comment | added | Mtheorist | A relevant paper - projecteuclid.org/download/pdf_1/euclid.cmp/1104249532 | |
| Aug 2, 2018 at 9:15 | comment | added | Xenomorph | Hi @ Sunghyuk Park Would you give me some references talking about details of the deformation? | |
| Aug 2, 2018 at 0:29 | comment | added | Henry | Moreover, $SL(2,\mathbb{R})$ being contractible to $U(1)$ means that any vector bundle with structure group $SL(2,\mathbb{R})$ can be smoothly deformed to a vector bundle with structure group $U(1)$. Because first Chern classes take discrete values, statements on page 13 about $U(1)$ bundles should carry over immediately to the case of $SL(2,\mathbb{R})$ bundles. | |
| Aug 2, 2018 at 0:13 | comment | added | Henry | I guess $SL(2,\mathbb{R})$ Chern-Simons theory should be equivalent to $SL(2,\mathbb{C})$ Chern-Simons theory with structure group restricted to $SL(2,\mathbb{R})$. So given a representation of $SL(2,\mathbb{R})$, we can complexify that representation, and there must be the associated complex vector bundle. Then we can talk about second Chern class, etc. | |
| Aug 1, 2018 at 23:18 | history | edited | Xenomorph | CC BY-SA 4.0 |
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| Aug 1, 2018 at 23:11 | history | asked | Xenomorph | CC BY-SA 4.0 |