I know that many quantum field theories could be low-energy effective theories in String Theory (ST), but I've also read and heard that ST cannot itself be an effective theory.

I suppose this has something to do with the UV behaviour of scattering amplitudes in ST and its conformal properties. Is it known to be impossible, though, for ST to be a (e.g. low energy) limit of another theory? If so, why? Is there merely consensus amongst experts or is there a rigorous proof?

I can't see of any motivation for considering ST to be an effective theory, since it's supposed to explain everything without any adjustable parameters. I'm just curious about this point.

  • $\begingroup$ +1 on the remark "I can't see of any motivation, I am just putting my finger here into your eyeball just for curiosity" :-D $\endgroup$
    – arivero
    Sep 28 '15 at 23:55
  • $\begingroup$ You could treat a string theory as an effective theory, an effective theory of the QCD flux tube for example. See this paper: arxiv.org/abs/1405.6197. $\endgroup$ Mar 8 '16 at 2:32
  • $\begingroup$ what about higher spin gauge theory? $\endgroup$
    – John Doe
    May 19 '16 at 18:23

Considering scattering amplitudes it's commonly believed that string theory is UV-finite, so it gives you the exact answer that you are seeking, at whatever energy level, without needing approximations (at least in principle, in practice we know mainly perturbation theory). Intuitively, the UV finiteness is due to the finite size of the string. To be clear, there isn't a formal proof of these statements.

However the full non-perturbative picture is still unclear. For instance the IIA superstring theory - and using $S$, $T$ and $U$ dualities all other superstring theories - can be seen as a $g_s\lll1$ limit ($g_s$ is the closed string coupling constant) of the eleven dimensional M-Theory.

Indeed a bunch of $n$ D0-branes in IIA can be seen as a bound state at threshold (the branes are BPS objects, so repulsion equals attraction), with mass:

$$M=\frac{n}{g_s \alpha'}$$

This is the typical mass spectrum $M=n/R$ of Kaluza-Klein with radius $R$. So $R_{11}=g_s \alpha'$ is another dimension that opens up in the $g_s\ggg1$ limit, and the D0 branes can be seen as Kaluza-Klein particles of M-theory.

  • $\begingroup$ This is very interesting information about the UV behaviour, but I'm not sure it exactly answers my question. Are you saying that all STs are effective theories of M-theory? If so, can M-theory be an effective theory too? $\endgroup$
    – innisfree
    Sep 28 '15 at 23:48
  • $\begingroup$ Actually the $g_s>>>1$ limit is different from the UV regime (it's more like the QCD at low energies). What I wanted to stress is that even though we claim string theory to be UV finite, there is a broader picture that we still not understand. In some sense string theory emerge as a sub-theory of M-theory and it's not excluded that we will discover more fundamental theories. Considering this "string-M-F-ecc." theory, there is no motivation to see it as an effective theory, as I've already said. $\endgroup$
    – Rexcirus
    Sep 29 '15 at 8:21

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