CAN STRING THEORY BE VERIFIED?

The so-called (super)string theory (SST) is a theoretical framework based on physics and mathematics that constitutes our best candidate for achieving the "holy grail" of fundamental physics: unifying the four forces of nature and achieving a quantum theory of gravity. The question everyone asks when they hear about string theory is: Can it be verified or refuted experimentally?

The answer to this question is affirmative, albeit with nuances: its experimental verification will be very difficult and will depend on whether the evidence confirming or refuting it is clear enough to directly associate it with "string" effects, differentiating them from other possible phenomena.

In this article, we'll analyze possible ways to verify string theory, classifying them into three groups: cosmological observations, observations of new particles, and observations of new physical phenomena. We'll also look at some possible ways to refute the theory.

Difficulties in verifying and refutation of string theory

The major challenge in finding experimental evidence to support TSC is that its natural scale, the scale on which its fundamental elements (strings and branes) "reside," is on the order of 10-35m. This energy scale is 1015 times larger than the one we can probe at the LHC.

Another major problem is that the vacuum configuration of the theory is not unique; in fact, there are on the order of 10,500 possible vacuums. This makes it very difficult to find unique configurations that give rise to a Universe like ours and that predict new, testable phenomena at low energy. This problem is like searching our Universe for the low-energy "remnants" of a theory that operates at the highest physically possible energy (the Planck energy) and is built in 10 dimensions of space-time. Despite the difficulties, there are several "fingerprints" or

Generic predictions that could indicate the theory is correct or even confirm or refute it. Below, we'll analyze these low-energy "fingerprints" predicted by CST.

Cosmological observations

- "moduli" scalar fields

Virtually all the various semi-realistic models based on CST predict the existence of scalar fields called "moduli." These fields generally arise from variations in the metric of the compactified extra dimensions. These fields, if they exist, can have important cosmological consequences. The moduli fields, when oscillating around their vacuum state,

produce non-relativistic matter with an energy density of D=1/a3 (where a is the expansion scale factor of the Universe) while the energy density of radiation is D=1/a4. Immediately after the Big Bang the Universe was dominated by the radiation produced by this "explosion". Later, when the Universe cooled enough, primordial nucleosynthesis occurred, where certain amounts of H, He and Li were produced by nuclear fusion. From that moment on the Universe became dominated by matter. The key point is that if the moduli fields exist, part of the energy generated in the Big Bang would be absorbed by these fields, producing more matter, so that the Universe would have had a transitory phase of matter domination before primordial nucleosynthesis.

This fact would have effects that could modify the predictions of the currently accepted standard cosmological model. For example, predictions for the indirect search for dark matter WIMP particles could be significantly affected, since these particles could be generated directly by moduli decay. These effects could be observed in future cosmological observations and in dark matter search experiments.

- Pseudo-scalar axion fields

Similar to moduli fields, compactifications of extra dimensions produce a large number of axions with very diverse characteristics. This entire range of axion-like particles is called "the axiverse." We can say that CST predicts the existence of an entire axiverse. These axions with different characteristics could leave their "fingerprints" in three different fields of cosmology:

1-Cosmic inflation: Axions form the fundamental ingredient that allows the SST to develop an inflationary phase that would give rise to a Universe like our own. Future observations could support or rule out an axion-based inflation model (and perhaps the type of axions favored by the SST).

2- Dark matter: Like moduli fields, axion fields oscillate, behaving like non-relativistic mass, which makes them ideal candidates for forming dark matter. The axions predicted by SCT may have distinctive features different from those predicted by other theories such as QCD and

They may constitute more exotic candidates to explain dark matter (the so-called "fuzzy dark matter") such as the so-called "glue-balls" (confined states of "dark" gluons that can even interact with each other) that could solve cosmological problems such as the "core/cusp" problem observed in certain galaxies.

3- Dark radiation: Axion fields generate "dark" radiation (so called because dark matter is invisible). This radiation could have affected the abundance of light elements created during the nucleogenesis of the Big Bang. Furthermore, this dark radiation could constrain particle-based dark matter.

supersymmetric.

New particles

- Axions

As we saw in the previous section, TSC models predict the existence of a wide variety of axions. TSC postulates the existence of 10 dimensions of space-time. The 6 dimensions that we do not see are compactified into a minuscule size, which explains why we have not yet detected them. There are many different ways to compactify the 6 dimensions, but all of them involve the emission of particles called axions. The axion is a particle that can "mix" with the photon and is characterized by a mass and a coupling constant f. The so-called strong CP violation problem of QCD also predicts the existence of these particles, but they predict an upper limit for f: f < 1012. Therefore, the detection

of axions with f greater than this limit would be a distinctive "fingerprint" of SST. Furthermore, as we saw in the previous section, this limit has cosmological consequences that could be detected in the short term. Another difference is that string theory, unlike QCD, predicts a wide variety of axions with different characteristics.

- Z' particles

String theory predicts the existence of new particles called Z' due to their resemblance to the Z boson, one of the bosons that transmits the weak force. However, other theoretical models also predict the emergence of new Z' particles, such as grand unified theories, multiple Higgs models, and certain extensions of the Standard Model. Future precision accelerator experiments may be able to distinguish the "signature" of the TSC by analyzing the characteristics of the Z' and the physical phenomena that produce this boson.

- New Higgs particles

The discovery of new Higgs particles, or Higgsinos (their supersymmetric equivalent), would clearly indicate the existence of new physics and would give rise to a whole range of new particles and phenomena. The TSC predicts the existence of a whole series of new Higgs-Higgsinos with distinct characteristics.

- Exotic particles

There is the possibility of the existence of "exotic" particles that appear to cancel out anomalies due to symmetry groups larger than those of the SM. The TSC allows for the existence of these particles with different characteristics.

- Leptoquarks, diquarks, dileptons and Rp violations

The SST allows for leptoquark, diquark, or dilepton coupling between hypothetical exotic particles and the SM. These phenomena would manifest themselves through violations of the SM rules (flavor physics violations, B-decay anomalies, etc.). Therefore, the presence of these particles could be a "fingerprint" of the SST.

Observations of new phenomena

- New gauge symmetries and hidden sectors

The so-called Standard Model (SM) is our current theory that explains practically everything we know about particle physics. This theory is based on the SU(3)xSU(2)xU(1) gauge symmetry. There are several theories that postulate the existence of larger symmetry groups such as SU(5), SO(10), etc. that would give rise to new conserved charges and therefore new particles. These new particles could form what are called "hidden sectors" because we would only see their effects due to their coupling to the SM. The SST has characteristic symmetry groups such as E8xE8 or SO(32).

By analyzing the effects of hidden sectors on the SM, it might be possible to discern which symmetry group they belong to and which theoretical model they best fit. If the hidden sector is weakly coupled to the SM (through gravity, moduli, or axions), its effects will be difficult to see, but if it is strongly coupled, its effects could be clearer and could produce "dark particles" such as glue balls or dark hadrons, with implications for the search for dark matter.

- No universality of the family

There are three lepton families in the SM. The TSC predicts a whole range of new families with different origins. This would produce violations in flavor physics, such as flavor changes across neutral currents. These effects could be detected at the LHC or in other experiments.

- New non-standard mechanisms for generating neutrino mass

The mechanism by which neutrinos acquire mass is still unknown. Several competing models exist to explain this, the validity of which will depend on certain neutrino characteristics yet to be confirmed. CST predicts new, non-standard mechanisms, primarily via "seesaws," due to the existence of new operators originating from extra dimensions.

- Existence of large extra dimensions

If one or more of the extra dimensions of the TSC were large, the natural scale on which strings manifest would be much larger, perhaps even on the TeV scale accessible at the LHC. If this were to happen, current or future searches at the LHC could find quantum gravity phenomena with the "fingerprint" of the TSC.

- Other phenomena

Other effects that could be indicators of the existence of "string-like" phenomena would be: violations of Lorentz and CPT symmetry, variation of the fundamental constants, absence of massless representations of continuous spin of the Poincaré group, the discovery of supersymmetric particles and the discovery of primordial cosmic strings.

Refutations of string theory

Grand Unified Theories (GUT)

The vast majority of TSC-based models are incompatible with the symmetries of GUT models due to the great difficulty in generating these symmetries and the lack of mechanisms capable of breaking them. Therefore, if GUT models were to be verified experimentally, the vast majority of TSC models would be shown to be incompatible with observations.

Existence of large representations

The CST does not allow for the existence of large representations of symmetry groups at low energy. Therefore, if large or unusual representations were discovered in experiments, this would be a very strong indicator against the validity of the CST.

Conclusions

The popular belief that string theory makes no experimentally testable predictions is completely false, although it is true that, by the very nature of the theory, they are difficult to verify. This, of course, does not hold anything against it; nature simply is as it is, regardless of our

desires or preferences. In addition, something very important must be taken into account: string theory is already producing important practical results in several branches of Physics and Mathematics (quark-gluon plasma physics, solid state physics, dualities, amplitude calculation techniques, etc.) to the point that in the

LHC software is already using techniques based on calculations derived from the TSC. Furthermore, the knowledge gained about certain characteristics that any quantum theory of gravity must meet is invaluable.

Therefore, even if string theory were not the expected "theory of everything," the knowledge it generates would still be enormously valuable. Of course, we all hope that string theory will reveal to us what is undoubtedly the deepest and most transcendent knowledge of the laws of physics: the ultimate nature of space-time.

Sources: Remnants from the String Landscape