Kane in Physics Today, “String theory and the real world”

“String theory solutions make unambiguous, testable predictions about our four-dimensional universe. To test string theory is like to test Newton’s second law F = ma (a relation between the force F on a particle with mass m and its acceleration a), every test requires a presumed force to be compared with the measured value. The test will fail if either Newton’s law or the presumed force is wrong. F = ma cannot be tested without recourse to positing forces and looking at actual solutions, similarly with string theory. Properties of the real world test the overall string framework and, at the same time, “compactifications” analogous to the forces of Newtonian mechanics or the Hamiltonian of quantum mechanics.” It is the opinion of Gordy Kane (director of the Michigan Center for Theoretical Physics & University of Michigan in Ann Arbor), “String theory and the real world,” Physics Today 63: 39-43, Nov. 2010 [free copy].

String theory (or M-theory) is only a framework, since “there is not yet a final formulation of the theory,” but it can be used “to address many issues facing particle physics and cosmology. String theory address but do not explain the standard model, like supersymmetric extensions of the standard model address but do not explain the dark matter of the universe. Indirect evidence suggests that supersymmetry is a symmetry of nature at the TeV energy scale, but it can’t be exact at low energy (supersymmetry is a broken symmetry with superpartners having masses different from those of the known particles). If that picture is correct, it is likely that some of the superpartners of the known particles will be observed at the LHC. The lightest of the superpartners is typically stable against decay into standard-model particles, and calculations confirm that it can have the right properties to be the dark matter of the universe. Thus the supersymmetric standard model addresses the problem of dark matter: If physicists did not know about dark matter, the model would suggest it and indicate how to look for it. Similarly, string theory provides a framework to address and relate many open questions in particle physics. We know that particles divide into three families exemplified by the electron, muon, and tau, but if we didn’t know it, string theory would suggest that families exist and why. If we did not know about forces such as the strong and electroweak forces of the standard model, or the parity violation of the weak interactions, or supersymmetry, or inflation, or gravity, string theory would suggest them.”

To illustrate the difference between to address and to explain, “let us consider the proton. Quantum chromodynamics (QCD), a part of the standard model, is a theory of the strong interactions in which quarks interact via a force mediated by gluons. The QCD Lagrangian does not contain the proton explicitly. However, study of the QCD force reveals that bound states of quarks form. In particular, QCD requires the existence of a state that has all the properties—electric charge, spin, and so forth—of a proton. Moreover, physicists have used lattice gauge theory to calculate the mass of the proton to about 3% accuracy. So QCD explains the proton: If it had not been known, QCD would have predicted its existence and properties.”

In Kane’s opinion, “string theory is testable in basically the same ways that other theories are. The majority of research into string theory is not focused on how the theory connects to the real world; fortunately, an increasingly active group of “string phenomenologists” are focusing on formulating a string-based description of the world and testing that understanding. They are already making testable predictions, and will increasingly do so.”

“String theory is formulated in 10 or 11 spacetime dimensions. The differences between the two versions are technical and have little effect on” string phenomenology. “In the 10D case, six small dimensions form a Calabi–Yau manifold, a space with well-studied mathematical properties, determining, in part, the physics that emerges from string theory, in particular the particle content and forces. In the 11D case, M-theory, the 7D space that remains small, called a G2 manifold, has somewhat different mathematical properties from the Calabi–Yau space.”

“A compactified string theory is analogous to a Hamiltonian (or Lagrangian) of a system. All areas of physics, including string theory, have general rules for deriving physics from a Hamiltonian, but one defines a particular theory only after specifying the Hamiltonian, or perhaps forces. Physical systems are described not by the Hamiltonian but by solutions to the equations calculated from it. The key point is that solutions to the theory are the things tested. It’s a point that is often ignored, even by experts, in popular discussions.”

“It is simply wrong to say that string theory is not testable in basically the same way that F = ma or the Schrödinger equation is testable. To make contact with the real world, a 10D or 11D string theory must be compactified. String theories with stable or metastable ground states usually also have supersymmetry, so the compactification process must break that symmetry. Sometimes the compactification is consistent with what we know about the world and leads to additional, testable predictions about dark matter, LHC discoveries, and more.” Other times “it have generated wrong predictions and the theory failed. Specific examples can be find in talks accessible from the website of the international String Phenomenology 2010 conference held in Paris this summer or from that of the String Vacuum Project. ”

“One specific test of a compactified string theory involves neutrino masses. Joel Giedt, G. L. Kane, Paul Langacker and Brent D. Nelson, “Massive neutrinos and (heterotic) string theory,” Phys. Rev. D 71: 115013, 2005 [ArXiv], realized that a particular compactified string theory (showing three-family standard-like Z3 heterotic orbifolds), studied by Mary K. Gaillard and her PhD students (including Giedt and Nelson) at the University of California, Berkeley, in no case could generate light but not massless neutrinos (a simple seesaw mechanism does not arise). That work represents a clear example of a test of string theory. Although the particular compactification we studied did not yield the desired neutrino masses.”

“Sometimes when people talk about testing string theory, they are referring to tests that apply to the full 10D or 11D theory without compactification. There are general tests for quantum mechanics and quantum field theory, perhaps string theory has such general tests, but that is not yet clear. The ideal goal is to formulate testable properties that hold for all compactified string theories with metastable or stable vacua, regardless of the form of the compactification or other conditions such as supersymmetry breaking. For example, string theory predicts an energy of the universe, or cosmological constant, that is much greater than observed. That discrepancy is one of the outstanding puzzles of theoretical physics.

“The cosmological constant is the value of an appropriate potential at its minimum, and in any particular string theory, it will scale with the product of the Planck mass and the mass of the gravitino, the supersymmetric partner of the massless graviton associated with the gravitational force. That result is too large a cosmological constant. In fact, for an M-theory compactified on a G2 manifold, implementing the potential tuning leads to only small numerical changes in the observables.”

“Bobby Samir Acharya, Gordon Kane, Eric Kuflik, “String Theories with Moduli Stabilization Imply Non-Thermal Cosmological History, and Particular Dark Matter,” ArXiv, 16 Jun 2010, proposed that nonthermal cosmic evolution is a general prediction for compactified string theories with broken supersymmetry and stabilized moduli. It apparently does not depend on the particular forms of the compactification, supersymmetry breaking, or stabilization. Moduli-based nonthermal cosmic evolution predicts that dark matter is the lightest superpartner, moreover, this particle is the wino—the superpartner of the W boson.”

“Let us first recall that moduli fields characterize the sizes, shapes, and metrics of the small manifolds (6D Calabi–Yau manifolds in a 10D string theory) and represent physical quantities. Once they take on definite values in the ground state they determine many measurable observables, such as interaction strengths and the masses of the gauge bosons that mediate the standard-model interactions. A modulus has quanta analogous to the photons associated with the electromagnetic field. Let us also recall that the gravitino is the superpartner of the graviton, the massless quantum associated with the gravitational field. When supersymmetry is broken, the gravitino becomes massive. Its mass sets the scale for all the other superpartners and for the moduli. String theories can have many moduli, with different stabilized values and masses, but at least one modulus whose mass is on the order of the gravitino mass.”

“Moduli interact only gravitationally and their lifetime is approximately calculable in terms of its mass. If even one modulus were to decay after the beginning of nucleosynthesis, the decay products would alter the abundances of helium and other nuclei that are successfully described by the usual theory that does not include moduli. Thus the moduli and gravitino masses must be at least 30 TeV or so to guarantee that the decay occurs early enough.”

“In fact, the moduli decay when the universe has cooled to a temperature of order 0.01 GeV, and in doing so they introduce large amounts of additional particles. These new particles and dark matter lead to several testable predictions. Immediately after the inflationary epoch, the universe is matter dominated—by the moduli—not radiation dominated as in the usual model. The dark matter is not present until about 0.01 s after the Big Bang. The amount of dark matter is fixed by the time when dark matter freezes out, that is, when it is cold enough and the universe has expanded enough that dark-matter particles are unlikely to encounter one another.”

“In order that theoretical physicists claim to fully understand string theory, they must understand the existence and implications of the string theory landscape—that is, its enormous number of solutions that could potentially describe the universe.  t question. What matters is that the predictions of the 10D theory for the 4D world are demonstrably testable and falsifiable. If no compactified string theory emerges that describes the real world, physicists will lose interest in string theory. But perhaps one or more will describe and explain what is observed and relate various phenomena that previously seemed independent. Such a powerful success of science would bring us close to an ultimate theory.”

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