Timeline for Is String Theory proven to be finite?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 9, 2013 at 4:59 | vote | accept | Graviton | ||
| Jul 8, 2013 at 2:22 | comment | added | Graviton | @UrsSchreiber, there are plenty of arguments that the (super-)string is UV-finite at each order and this argument is regarded as robust -- so this means that although sound arguments were purposed, but they are not definite mathematical proofs on the finiteness each terms in pertubation series, am I right? | |
| Jul 4, 2013 at 21:01 | comment | added | MBN | @Graviton: you may want to look up asymptotic series. | |
| Jul 4, 2013 at 16:43 | comment | added | Urs Schreiber | I have been expanding the relevant nLab entries a little more, also adding more pointers, see here: ncatlab.org/nlab/show/… | |
| Jul 4, 2013 at 15:24 | comment | added | Graviton | @MitchellPorter, maybe you would like to expand your comments into an answer? | |
| Jul 4, 2013 at 15:24 | comment | added | Graviton | @UrsSchreiber, would you like to incorporate your comments into your answer? | |
| Jul 4, 2013 at 15:08 | comment | added | Manishearth | A note: If you feel that this discussion is going to be long (it's OK right now, a few more comments wouldn't hurt, but >10 comments can be unweildy), I encourage you to create a room in Physics Chat, link to it here, and continue. As such, chat is better equipped than comments for discussion. Thank you ) | |
| Jul 4, 2013 at 13:57 | comment | added | Urs Schreiber | Mr. Graviton, this may be a shock now: also QCD perturbation theory is divergent. See for instance this Physics.SE discussion: physics.stackexchange.com/q/30105/5603 . Every sensible QFT diverges perturbatively. | |
| Jul 4, 2013 at 13:48 | comment | added | Mitchell Porter | Divergence of a perturbation series can mean that there are extra terms needed to make the series converge, or that the starting point was wrong. Extra terms can come from branes, while "wrong starting point" here would mean that some other background geometry is the stable one. These discussions of "whether string theory is finite" revolve around the finiteness of individual terms in the perturbation series. The problems of the bigger context are "nonperturbative" issues. | |
| Jul 4, 2013 at 13:43 | comment | added | Graviton | Sorry, but I still don't get it. The reason why we use an infinite series to represent a physical quantity is because we believe that after summing up the series, we will come to get a finite number. If not, we would say that the theory breaks down and the physical quantity is not computable from the theory. So in order to avoid negative coupling constant which is unphysical, then we allow the sum to be infinite? Then what does this tell us of string theory predictability power? | |
| Jul 4, 2013 at 13:34 | comment | added | Urs Schreiber | As the next sentence says, the perturbation series of any sensible QFT has vanishing radius of convergence. So, no, this divergence of the sum is a sign that string perturbation theory is healthy, convergence here would be unrealistic. See ncatlab.org/nlab/show/… | |
| Jul 4, 2013 at 13:15 | comment | added | Graviton | Remark 1 says that "This sum diverges, even if all loop orders are finite."-- so I guess it means that the summing of all the pertubative terms in string theory is infinite, which means that string theory can't converge, and hence infinite, and hence cannot be physically real, right? | |
| Jul 4, 2013 at 11:13 | history | answered | Urs Schreiber | CC BY-SA 3.0 |