String Theory Searches for the Standard Model
String theory offers the possibility of a route to the "Theory of Everything." It contains all of the ingredients that we see in nature: quarks, leptons, photons, gluons, and gravity. For a long time, string theorists hoped that their equations would have a unique solution describing the real world. In fact, it is not so. The equations of string theory have a huge number of solutions, and we are finding more every day.
The present surge of new results followed the insights of SLAC and Stanford University's Shamit Kachru, Renata Kallosh, and Andrei Linde, as well as the Tata Institute’s Sandip Trivedi. The work of these researchers provided a method for constructing a large number of distinct solutions to string theory.
String theory requires space-time to have ten dimensions. To obtain a universe that appears four-dimensional, the researchers looked for solutions in which the other six dimensions are wrapped up as a specific type of compact space called a Calabi-Yau manifold. To this geometry they then added various loops and sheets (called branes) that wrapped around the Calabi-Yau manifold, and various types of electric and magnetic fields that threaded along smooth closed paths. Kachru and his collaborators argued that there exist a huge number of solutions of this typeat least 10500, by some estimates.
We do not understand how to deal with this multitude of solutions. No solution has been found yet that contains the Standard Model of particle physics. Maybe such a solution (one or more) is buried in this huge ensemble; but perhaps not. It is possible that string theory predicts only the statistical properties of the ensemble. If this is the case, the presence of the Standard Model and the mass of the top quark would be historical accidents.
The only way we will get a better understanding is to plunge in and learn how to explicitly construct solutions with the desired properties. Burt Ovrut and collaborators at the University of Pennsylvania have made progress using an abstract mathematical approach, the study of holomorphic vector bundles over Calabi-Yau manifolds. Abstract as this may be, it is a useful tool. Here at SLAC, Shamit Kachru, Peter Svrcek and I, with Duiliu Diaconescu of Rutgers University, used this technology to construct string models in which the supersymmetry is spontaneously broken and that breaking is conveyed by gauge interactions to make the superpartners of quarks and leptons heavy.
I am now working with Shamit Kachru and John McGreevy at SLAC and Natalia Saulina of Harvard University on other approaches to breaking supersymmetry in string theory. Our approach uses the detailed six-dimensional geometry of the Calabi-Yau manifolds. Often, the manifold has a singularity. Branes on the manifold can smooth out the singularity by deforming it, and the smoothed configuration leads to a model of particle physics with supersymmetry. Sometimes, though, there can be a geometric barrier to the deformation. In these cases, the particle physics model has spontaneously broken supersymmetry. It is very tricky to analyze whether the barrier is absolute or whether quantum effects can tunnel through it. But in certain models, we can prove that tunneling is impossible.
These models add new possibilities to string theory solutions, making the problem of interpreting string theory harder, not easier. Can we converge on a string theory that describes our real world? Is there a reason to find this particular solution, or one like it? We still need to learn much more before we can answer these questions.