Timeline for Why are CFT descriptions of String Theory inherently perturbative and how can it be circumvented?
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| May 7, 2016 at 17:27 | comment | added | Thomas | @CGH : 1) "the theory contains non-perturbative phenomena, it does not mean that the theory is non-perturbative" ???? 2) In QCD the sum over all scatterings is not just incomplete, it is divergent and ill-defined. 3) We know how to define the path integral, not how to compute it (except numerically). | |
| May 7, 2016 at 3:48 | history | edited | CGH | CC BY-SA 3.0 |
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| May 7, 2016 at 3:42 | comment | added | CGH | Thomas. the existence of instantons just means that the theory contains non-perturbative phenomena, it does not mean that the theory is non-perturbative, nor that the sum over all possible scatterings is incorrect (it just says that is incomplete). In ST the "instantons" might be called D-branes. I'm not saying that they are the same, or that this is the final answer. Non-perturvative effects in string theory is one of the many unanswered questions in ST. Finally, if the full non-perturbative QCD is known, why there's no proof of confinement? I think you are overreaching. | |
| May 7, 2016 at 3:29 | comment | added | CGH | user1504: 1) Yes, it is true, I just went too far too fast. QED is not well defined in the IR, and due to a lapsus I just put the solution to that as QCD. It is an effective theory of the electro-weak model, where the mass of the $Z$ and $W^\pm$ bosons are integrated out. 2) It is true that ST and QFT are different, but I just pointed out that the "perturvative" nature of ST that quantif gave can be compared with the QFT case. I just draw an analogy between them. | |
| May 7, 2016 at 1:24 | comment | added | Thomas | @CGH : Correlation functions have non-perturbative contributions, such as instantons. In QCD we have a definition of the full non-perturbative correlation function, thanks to Wilson's lattice formulation of the path integral. In string theory, no analogous definition exists. | |
| May 6, 2016 at 23:46 | comment | added | user1504 | 2) Your answer to the main question obfuscates a critical difference between string theory and QFT. In QFT, we have an essentially complete description of scattering amplitudes and we have perturbative approximations to them. In string theory, we're missing much more. In most situations, the perturbation theory is all we have. (There's an essentially complete definition in matrix theory, but the form of it is in general unknown.) | |
| May 6, 2016 at 23:41 | comment | added | user1504 | 1) QED isn't an effective field theory for QCD. They describe different physical phenomena. | |
| May 6, 2016 at 22:41 | comment | added | CGH | Thomas, the "time ordered correlation function" is just a sum over all possible scatterings. | |
| May 6, 2016 at 21:10 | comment | added | Thomas | "Amplitudes, in any QFT, is defined a sum over all possible scatterings." I don't think that's correct. Amplitudes are defined by time ordered correlation functions, which have non-perturbative definitions via the path integral. In particular, amplitudes can have genuinely non-perturbative contributions, that are not just the sum over all scatterings. | |
| May 6, 2016 at 19:22 | history | edited | CGH | CC BY-SA 3.0 |
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| May 6, 2016 at 19:13 | history | answered | CGH | CC BY-SA 3.0 |