Michael B. Schulz: Research Interests - Motivations

What are the fundamental building blocks of matter? How do they interact? When did it all begin, and was there even a beginning?

In each generation in every society, answers are offered to these profound questions. Over the last century, the methods of elementary particle physics and cosmology have woven an intricate story that has done much to answer the what and how. Within the framework of quantum field theory, the standard model of particle physics describes all non-gravitational phenomena in our universe using only a handful of elementary particles and three forces—the electromagnetic, strong, and weak interactions. In every case that the predictions can be calculated, they agree with observation to unprecedented numerical accuracy. The remaining force, gravity, is described by general relativity. By combining general relativity with input from the standard model, and with the help of the current era of precision observational astronomy, cosmologists have built a compelling case for the history of our universe, replacing the earliest moments of the hot big bang model with a preceding period of rapid expansion. It is during this inflationary period that the seeds of galaxies were sown. Still, the question why remains. Why is the universe the way it is? Why are the laws of nature as they are and not otherwise?

The why question becomes all the more alluring in light of several shortcomings of the standard model plus general relativity — shortcomings which suggest that the laws as we now know them are not the final say. It is the resolution of these shortcomings to which I hope to contribute through my research, primarily in the context of string theory. Here are a few of the problems:

1. The problem of quantum gravity

Any combination of general relativity with the standard model is inherently ad-hoc, since the latter is a quantum theory and the former not. Moreover, the naive solution, a quantum field theory of general relativity is inconsistent. The problem has to do with short distances. From magnifying glasses to electron microscopes to particle accelerators, objects (light, electrons, nuclei) of ever decreasing wavelength and ever increasing energy are used to probe smaller and smaller distances. In quantum field theory, this refinement can continue indefinitely, but general relativity sets a limit. (The best one can do at minimizing both the Compton wavelength and Schwarzschild radius of a particle is the Planck length, LP = (G h/c3)1/2.) Too much energy in too small a space yields a black hole, a region of space impervious to outside observation. Therefore, a quantum theory of our universe — which includes gravity — should be something that generalizes quantum field theory at very small distances, but that reduces to it at larger distances.

2. The hierarchy problem

In the standard model, the electromagnetic and weak interactions unify into a single electroweak force above a phase transition at high energy. This phase transition also gives the elementary particles their mass. In contrast, quantum gravity becomes important at the tremendously higher Planck energy. The hierarchy between the two begs explanation. If there is no new physics between the electroweak scale and the Planck scale, then the hierarchy is unnatural.

3. Matter in our universe

In addition to the visible matter that the standard model describes, we now believe that there is roughly six times as much dark matter in the universe that it cannot account for. The evidence comes from observations of galaxy rotation and of the cosmic microwave background. Moreover, even for the visible baryonic matter (this includes protons, neutrons and atomic nuclei), there is a problem. The universe contains many more protons than antiprotons. It contains galaxies but not antigalaxies. The standard model alone cannot explain this. It cannot explain baryogenesis, the origin of the matter/antimatter asymmetry observed in our universe.

The most conservative explanation of both the hierarchy problem and dark matter is to assume that some extension of the standard model, with new particles and new interactions, becomes relevant at energy scales not far above the electroweak phase transition. The dark matter is made up of the lightest new particles that are stable to decay to standard model matter. To be viable, the extension should also be rich enough to contain a mechanism for baryogenesis. We can add a wish as well:

4. Uniqueness — the why problem

The standard model of particle physics includes a seemingly arbitrary spectrum of particles, forming a ``periodic table'' of three families and interacting through a similarly arbitrary choice of forces. Why? Other choices are also consistent, albeit in a very different world from the one we know. The hope is that a more fundamental theory would reduce the number of arbitrary choices, ideally to none.

To be pragmatic, we can wish for greater uniqueness in our theory of nature, but aim for a more modest goal: (i) to address tangible problems like the hierarchy problem, baryogenesis, and the existence of dark matter through an extension of the standard model, and (ii) to construct a consistent gravitational quantum theory that reduces to this extension plus general relativity at sufficiently large distances.

My research focuses primarily on (ii), within the framework of string theory. String theory is an approach to quantum gravity in which the point particles of elementary particle physics are replaced by small vibrating strings. There is every indication that this modification cures the short distance problem of quantum field theory plus general relativity in a consistent way. Moreover, there is a natural limit in which string theory reduces to quantum field theory plus general relativity in spacetimes that are only weakly curved. The different solutions or vacua of string theory lead to different quantum field theories. My work seek to generalize the toolbox through which realistic quantum field theories like the standard model and its extensions can be ultimately be realized as large distance limits of string theory vacua. (Does string theory solve the why problem? In a technical sense yes: it is a unique theory. It has no freely tunable parameters, continuous or discrete. But, in a practical sense, the verdict is still out. The theory does seem to have many consistent solutions. It is not yet known whether a dynamical mechanism exists that could select a particular solution corresponding to our universe.)

Toward (i), we are entering an era in which a new experiments will be a real guiding light. The Large Hadron Collider (LHC)—a particle accelerator in its final stages of construction in Geneva, Switzerland—will take the first really great leap forward in twenty years, in probing nature at higher energies and short distances. We expect to observe directly how the standard model is modified at energies just above the electroweak phase transition. This is an exciting time, in which experiment will decide among conflicting theories. In the future I expect to devote a part of my research to studying aspects of extensions of the standard model that can be tested at the LHC. (For a step in this direction, see this page.)