String Theory has many problems.
It has six (or in some accounts seven) space-time dimensions too many. It predicts lots of new supersymmetric particles and forces (even without adding in gravity) that we haven't observed (experimental exclusions for such particles were reviewed at this post). It needs to explain why we don't observe proton decay. It predicts a scalar-tensor theory of gravity that isn't observed. It is happiest in an "anti-deSitter" universe which is roughly equivalent to a negative cosmological constant when the measured value of the cosmological constant of General Relativity is positive. The physics journalist for Forbes magazine recaps these issues.
Ethan Siegel has an excellent piece on the basic problem with string theory (to the extent it’s well-defined, it has too large a (super)symmetry group and too many dimensions, no explanation for how to recover 4 space-time dimensions and observed symmetry groups).Here’s why the hope of String Theory, when you get right down to it, is nothing more than a broken box of dreams.
From Not Even Wrong.
[T]here are a lot of symmetries that you could imagine would be respected, but simply aren’t. You could imagine that the three forces of the Standard Model would unify into a single one at high energies in some sort of grand unification. You could imagine that for every fermion, there would be a corresponding boson, as in supersymmetry. And you can imagine that, at the highest energies of all, that even gravity gets unified with the other forces in a so-called “theory of everything.”That’s the brilliant, beautiful, and compelling idea at the core of String Theory. It’s also has absolutely no experimental or observational evidence in favor of it at all. . . .
Many ideas — such as grand unification and supersymmetry — would involve adding new particles and interactions, but would also lead to experimental consequences like proton decay or the presence of additional particles or decay pathways not seen at colliders. The fact that these predictions haven’t panned out helps us place constraints on both of these ideas.String theory, though, goes many steps farther than either grand unification or what we know as supersymmetry does.For grand unification, the idea is to take the three forces in the Standard Model and embed them into a larger, more symmetric structure. Instead of the particles we know with the interactions we know — with multiple disjoint frameworks corresponding to each of the forces — grand unification tries to fit the Standard Model inside a larger structure.This might just sound like words to you, but the group theory representation of the Standard Model is SU(3) × SU(2) × U(1), where the SU(3) is the color (strong force) part, the SU(2) is the weak (left-handed) part, and the U(1) is the electromagnetic part. If you want to unify these forces into a larger framework, you’ll need a bigger group.You can take the route of Georgi-Glashow [SU(5)] unification, which predicts new, super-heavy bosons that couple to both quarks and leptons simultaneously. You can take the route of Pati-Salam [SU(4) × SU(2) × SU(2)] unification, which adds in the right-handed particles, making the Universe left-right symmetric instead of preferring a left-handed neutrino. Or you can go even larger: to SU(6), SO(10), or still larger groups, so long as they contain the Standard Model within them.The problem, of course, is that the larger you go, the more stuff there is to get rid of, and the more explaining there is to do if we want to understand why these extra components to reality don’t show themselves, either directly or indirectly, in our experiments, measurements, and observations of the Universe. The proton doesn’t decay, so either the simplest model of grand unification is wrong, or you have to pick a more complicated model and find a way to evade the constraints that rule out the simpler models.If you want to talk about unification and group theory in the context of String Theory, however, your group suddenly has to become enormous! You can fit it into one of the SO groups, but only if you go all the way up to SO(32). You can fit it into two of the exceptional groups crossed together — E(8) × E(8) — but that’s enormous, as each E(8) contains and is larger than SU(8), mathematically. This isn’t to say it’s impossible that String Theory is correct, but that these large groups are enormous, like a block of uncut marble, and we want to get just a tiny, perfect statuette (our Standard Model, and nothing else) out of it.Similarly, there’s an analogous problem that arises with supersymmetry. Typically, the supersymmetry you hear about involves superpartner particles for every particle in existence in the Standard Model, which is an example of a supersymmetric Yang-Mills field theory where N=1. The biggest problem is that there should be additional particles that show up at the energy scales that reveal the heaviest Standard Model particles. There should be a second Higgs, at least, below 1,000 GeV. There should be a light, stable particle, but we haven’t observed it yet. Even without String Theory, there are many strikes against N=1 supersymmetry.The Standard Model, without supersymmetry, is simply the N=0 case. But if we want String Theory to be correct, we need to make nature even more symmetric than standard supersymmetry predicts: String Theory contains a gauge theory known as N=4 supersymmetric Yang-Mills theory. There’s even more stuff to hand-wave away if we want String Theory to be correct, and it all has to disappear to not conflict with the observations we’ve already made of the Universe we have.But one of the biggest challenges for String Theory is something that’s often touted as it’s big success: the incorporation of gravity. It’s true that String Theory does, in a sense, allow gravity to be merged with the other three forces into the same framework. But in the framework of String Theory, when you ask, “what is my theory of gravity,” you don’t get the answer that Einstein tells us is correct: a four-dimensional tensor theory of gravity. . . .So what does String Theory give you? Unfortunately, it doesn’t give you a four-dimensional tensor theory of gravity, but rather a 10-dimensional scalar-tensor theory of gravity. Somehow, you have to get rid of the scalar part, and also get rid of six extra (spatial) dimensions.We had, as proposed 60 years ago, an alternative to Einstein’s General Relativity that did incorporate a scalar as well: Brans-Dicke gravity. According to Einstein’s original theory, General Relativity was needed to explain the orbit of Mercury, and why its perihelion (where it came closest to the Sun) precessed at the rate that it did. We observed a total precession of ~5600 arc-seconds per century, where ~5025 were due to the precession of the equinoxes and ~532 were due to the other planets. Einstein’s General Relativity predicted the other ~43, and that was the slam-dunk prediction he finally made in 1915 that catapulted the eclipse expedition into infamy. The 1919 revelation that light bent starlight was the ultimate confirmation of our new theory of gravity.But by the late 1950s, some observations of the Sun had indicated that it wasn’t spherical, but rather was compressed along its poles into an oblate spheroid. If that were the case, Brans and Dicke argued, then that observed amount of departure from a perfect sphere would create an additional 5 arc-seconds of precession per century that differed from Einstein’s predictions. How to fix it? Add in a scalar component to the theory, and a new parameter: ω, the Brans-Dicke coupling constant. If ω was about 5, everything would still turn out right.Of course, the Sun actually is a perfect sphere to a much better degree than even the Earth, and those observations were incorrect. Given the modern constraints that we have, we now know that ω must be greater than about 1000, where the limit as ω → ∞ gives you back standard General Relativity. For String Theory to be correct, we have to “break” this 10 dimensional Brans-Dicke theory down to a four dimensional Einsteinian theory, which means getting rid of six dimensions and this pesky scalar term and the coupling, ω, all of which must go away.What all of this means is that if String Theory is correct, we have to start with a Universe that’s highly symmetric and very unlike the Universe we have today. This Universe, at some early time at very high energies, had 10 dimensions to it, had a scalar gravity component in addition to the tensor component, was unified into some very large group like SO(32) or E(8) × E(8), and was described by a maximally supersymmetric (N = 4) Yang-Mills theory.If String Theory is correct, then somehow — and nobody knows how — this ultra-symmetric state broke, and it broke incredibly badly. Six of the dimensions disappeared, and the scalar gravity component stopped mattering. The large, unified group broke very badly, leaving only our relatively tiny Standard Model, SU(3) × SU(2) × U(1), behind. And that supersymmetric Yang-Mills Theory broke so badly that we don’t see any evidence for a single supersymmetric particle today: just the regular Standard Model. . . .It may be interesting and promising, but until we can solve String Theory in a meaningful way to get the Universe we observe out of it, we have to admit to ourselves what String Theory truly is: a large, unbroken box that must somehow crumble in this particular, intricate fashion, to recover the Universe we observe. Until we understand how this occurs, String Theory will only remain a speculative dream.
There are additional problems that aren't discussed in the article.
One is the fact that we live in a universe with deSitter rather than anti-deSitter topology. Another is the fact that there are myriad possible versions called vacua, the vast majority of which have an anti-deSitter topology which are called the "swampland" because most of them are starkly incompatible with observed reality.
Another is the fact that experimental evidence has established that supersymmetry, which is a necessary sub-component of string theory, was conceived to solve a problem that we now know that it doesn't solve in the way that it was intended to, called the "hierarchy problem" because even if supersymmetric particles and extra Higgs bosons exist, the Large Hadron Collider has established that they are too heavy to solve the "problem" that they were devised to solve.
There may be glimmers of useful mathematical or physical insight that one can gain from studying it, but it is along the lines of the insights into English grammar and vocabulary that you get from studying French for a year or two, that has no meaningful connection to the real world and doesn't allow you to do anything worthwhile.
But in the end analysis, there is a substantial and growing faction of the fundamental physics community, including both professional physicists and educated laypeople like myself, who have concluded that String Theory and Supersymmetry are both dead ends that have wasted immense amounts of time and resources of a lot of very smart people.