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String theory is often said to be one possible way to a theory of everything. In that setting it must obviously not just encompass gravity, but everything described by quantum field theory also.

In particular it must describe the elementary particles and the three fundamental forces properly described by QFT.

It turns out though, that QFT is totally non rigorous when interactions are taken into account. String theory, on the other hand, as far as I know (and I can be totally wrong, because I've never really studied it) is a rigorous theory mathematically speaking.

So in a sense, string theory does solve the problems of mathematical rigor presented in QFT?

I'm not discussing whether or not String Theory actually describes nature considering things like supersymetry, the 10 dimensions and so forth. I'm actually trying to understand if from a mathematical standpoint the problems of rigor in QFT are solved in String Theory.

In other words: the interactions of fields described in QFT without any rigor can be recast with string theory in a rigorous form?

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    $\begingroup$ String theory's perturbative expansions are based on ribbon graphs (i.e. Riemann surfaces with boundary) rather than Feynman diagrams with linear edges, so it is expected that the notorious divergencies of quantized gravity would not emerge there. The other advantage is that various dualities allow to explore non-perturbative regimes (which we are not even sure exist for QFT). But in a sense string theory is "more" non-rigorous than QFT at this point, only toy models are formulated rigorously, nothing realistic. $\endgroup$ – Conifold May 3 '17 at 1:56
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    $\begingroup$ The problem is QFT and string theory are not mathematical rigor, rather some adhoc models in one while still working it out that it is predictive down to a great extent, and toy models with no predictions for the other. It's the physics not the theorems $\endgroup$ – Bob Bee May 3 '17 at 2:02
  • $\begingroup$ The short answer is no. Only a perturbative definition of string theory is available at the moment. You might be interested in looking at string field theory, e.g. here en.wikipedia.org/wiki/String_field_theory $\endgroup$ – Antoine May 3 '17 at 13:12
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    $\begingroup$ What makes you think there is no rigorous work on interacting QFT? In low dimensions, there are perfectly rigorous non-perturbative QFTs. And if you are willing to consider not completely relativistic theories, there are rigorous QFTs also in 3+1 dimensions. $\endgroup$ – yuggib May 3 '17 at 16:40

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