What are the advantages of string theory? I'm following Witten's essay and it seams that he only presented one advantage of string theory (the fact that there are no UV divergence).

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*Are there more advantages to string theory?


*It seems to me that there is no big difference in the principles between string an normal field theory's apart from the fact that we change the point particles to one dimensional particles (and by doing it some calculations become better). Is this really the case?
 A: There are a couple of levels to address the question at that could apply, and I'll try to touch on all of the main ones in a summary fashion.
What physics applications would string theory make possible if it were completely worked out?

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*String theory's strongest argument in its favor is that it is provides a path to a mathematically consistent way to integrate gravity with other fundamental forces and particles found in the Standard Model of Particle Physics in a quantum gravity theory. There are "no go" theorems that argue that this is a unique solutions, although it might contain loopholes that the "no go" theory doesn't rule out.


*String theory should, in principle, provide a first principles way of calculating all of the dozens of experimentally measured physical constants of the Standard Model and General Relativity from one or two experimentally measured physical constants, once the values of those one or two experimentally measured physical constants were determined. There has even been some progress in bounding the values of string theory's physical constants in the literature to at least an order of magnitude.


*String theory might reveal new "beyond the Standard Model" physics, particularly physics that is important at extremely high energies such as those present in the first moments after the Big Bang. For example, string theory is widely expected, if completely worked out, to reveal that supersymmetry exists at some high energy scale, to reveal the details of the neutrino's properties, to provide a candidate for dark matter particles that actually works, and to provide a mechanism by which the baryonic matter-antimatter asymmetry of the universe arose. It would also rule out any hypothetical theories of physics that are inconsistent with it.
What how would string theory advance physics theoretically, if it were worked out properly?

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*String theory provides a potential foundation for a "theory of everything" that reduces all of fundamental physics currently addressed by the Standard Model and General Relativity to the properties of fundamental strings, representing the ultimate case of physics reductionism.

What benefits does string theory provide now?

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*It provides employment for string theorists.


*It gives rise to focused mathematical research that may give rise to spin-off knowledge useful in non-string theory applications (e.g. doing complex QCD amplitude calculations).


*It helps physicists to evaluate what a solution to unsolved questions in fundamental physics might "look right" in light of what we do know about string theory, and thus advance hypothesis building.
Why does string theory provide so few benefits now?
These benefits are so minimal, and indeed "string theory" barely deserves the name "theory" because no one has managed to tame the basic mathematical concepts of string theory. There is no operationalized version of string theory which produces the particles and forces that we observe in reality, which does not produce particles or forces that have been ruled out experimentally, and which can be used to calculate observable quantities.
Realistically, the goal of working out string theory into a fully worked out operationalized theory is not imminent, as there are no published papers or pre-prints that come anywhere close to setting forth such a theory.
A: I will push back a little bit on the so few benefits now verdict. Sure, for many of the interesting observables we have no idea how to compute them. But the same can be said about the real time dynamics of QCD. It is often said that "QCD beat string theory" in the 1970s by describing the strong force more accurately but this is a misleading statement. It was a particular type of deep inelastic scattering experiment where perturbative QCD was successful. Then and now, the stringy approach was more successful at explaining things like Regge behaviour. To understand how they can both still be right, consider $O(N)$ models in $d = 4 - \epsilon$ from condensed matter. There are two very different perturbative ways to study these models. Often times, the $\frac{1}{N}$ expansion is close to experiment while the $\epsilon$ expansion gives garbage or vice versa. But if we were infinitely powerful at computing all the terms and resumming them, the results would be the same.
So what are some current benefits?
The main one I want to focus on is shining a light on the landscape of possible QFTs... see https://arxiv.org/abs/1312.2684 for some background. A great number of field theories appear on the worldvolumes of branes. This provides the only reliable construction of a certain 6d non-Lagrangian CFT so far. But even if we don't care abut six dimensions, this is a stepping stone to plenty of results about four dimensions. Compactifying this CFT on a Riemann surface led to the discovery of many theories known as class S. Apart from just finding out that these theories exist, the string viewpoint helps us do calculations in them. This is because of a web of weak-strong dualities from https://arxiv.org/abs/0904.2715 and other sources. There is also something called the AGT correspondence where instanton partition functions of 4d gauge theories can actually be mapped to purely 2d objects where calculations are much simpler. There is also something called the Bethe / gauge correspondence where spaces of supersymmetric vacua in four dimensions can be studied by turning them into integrable spin chains. I attended a talk today which used string theory to extend this correspondence to more theories. This reminded me of a paper from a couple years ago where strings explained a mysterious result in https://arxiv.org/abs/1607.04281 about breaking supersymmetry only to have it reappear at low energies. Versions of this are now believed to hold for theories that have a much better chance of being created in the lab.
