Timeline for Knots in 3d pure gravity
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2021 at 13:09 | comment | added | ɪdɪət strəʊlə | This thing is to be integrated over $U$ and $A$. This is not an effective action. The effective action is what remains of that after you've integrated over $U$. This is pure gravity (with an insertion). | |
| Nov 2, 2021 at 10:40 | comment | added | Sounak Sinha | The inserted Wilson line acts as a source. The effective action for the theory becomes $S_{CS}(A)-S_{CS}(\bar{A})+S_c(U,A,\bar{A})$. But this is not the action for pure gravity. | |
| Nov 2, 2021 at 10:07 | comment | added | ɪdɪət strəʊlə | Right, so if I understand correctly the content of 1306.4338, one integrates out the quantum mechanical system on the Wilson line (as also explained in a paper by Witten which they cite). Then at low energies, i.e. below the scale set by the particle that we integrated out, the theory with the Wilson loop insertion is still an effective theory for pure gravity. (It is ofc not a problem that this is only an effective theory since so is the CS formulation in general) | |
| Nov 2, 2021 at 9:49 | comment | added | Sounak Sinha | You can also interpret Wilson lines as conical defects in AdS. If the opening angle of the defect is big enough it can backreact on the geometry and change the topology of the spacetime. But again, they are interpreted as matter fields and should not be considered while computing the path integral. | |
| Nov 2, 2021 at 9:41 | comment | added | Sounak Sinha | You can look at 1306.4338 section IID where the authors show that the Wilson line for a closed curve in some highest weight representation can be reduced to the worldline path integral for a massive particle propagating in a closed loop in AdS. If the closed curve has the topology of a circle then it can be contracted to a point. But if there is a black hole, or if the curve has non trivial topology, then the path integral turns out to be more interesting. | |
| Nov 2, 2021 at 9:17 | comment | added | ɪdɪət strəʊlə | but the Wilson line is not made out of matter fields, it is only made out of the gravitational data, the spin connection and the vielbeine. Massive particles can only come into place if the Wilson line has endpoints (and that's also why their mass is related to the Wilson line representation). But a knot has, by definition, no endpoints. Hence there are no matter fields here. This also implies that including knots we remain in pure gravity. | |
| Nov 2, 2021 at 8:50 | history | answered | Sounak Sinha | CC BY-SA 4.0 |