Timeline for Explanations for mathematicians, about the falsifiability (or not) of string theory
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jun 10, 2013 at 20:38 | comment | added | Urs Schreiber | Sorry, broken link, try this one instead: ncatlab.org/nlab/show/string+scattering+amplitude | |
| Jun 10, 2013 at 20:37 | comment | added | Urs Schreiber | I didn't state any opinions (I could if you ask me for it... :-). Concerning finiteness: that's the point of string scattering amplitudes that they are finite, hence "already renormalized", see ncatlab.org/nlab/show/string+scatt for literature. That's why one says that perturbative string theory provides a "UV-completion" for gravity coupled to gauge theory (ncatlab.org/nlab/show/effective+quantum+field+theory). One can think of the higher massive string modes as naturally providing counterterms for the non-finite masslass scattering amplitudes of the effective low energy thory. | |
| Jun 10, 2013 at 16:07 | comment | added | user34821 | @urs: i once heard that certain feynman path integrals involved subtracting infinities...has this issue been completely mathematically resolved? if so, a precise reference would be appreciated. thank you also for the comments, but i was looking for mathematical examples, not opinions on the state-of-the-art | |
| Jun 10, 2013 at 12:01 | comment | added | Urs Schreiber | The remaining problem of course is that the theory given by these solid definitions is immensely rich and so working out of all the consequences and phenomena takes time. Compare for instance vertex operator algebra theory, which is a small subsector of the formulation of full 2d CFT: the definition itself is, while non-trivial, fully precise, but deducing all the resulting phenomena is hard and at any given time will involve, among the actual theorems, open questions, conjectures, guesses and handwaving. This concerns all the sub-phenomena of string theory such as mirror symmetry etc. | |
| Jun 10, 2013 at 11:58 | comment | added | Urs Schreiber | Even more is understood of course for the toy version of perturbative string theory given by the "topological string". Here 2d CFT is replaced by "non-compact" TQFT, which for historical reasons is known as "TCFT" ncatlab.org/nlab/show/TCFT As for perturbative string theory, this are solid definitions. | |
| Jun 10, 2013 at 11:56 | comment | added | Urs Schreiber | Perturbative string theory has a rather solid formalization: first formalize 2d CFT, then formalize the computation of correlators in 2d CFT by integration over moduli spaces, together that fully defines peturbative string theory. Both aspects are rather completely understood abstracty and in principle and to a fair extent worked out. Specifically on the former point we have some contributions in the book collection ncatlab.org/schreiber/show/… . | |
| Jun 10, 2013 at 9:46 | history | answered | user34821 | CC BY-SA 3.0 |