Special Section: Superstrings – a Quest for a Unified Theory

MANY of the major developments in fundamental physics of the past century arose from identifying and overcoming contradictions between existing ideas. For example, the incompatibility of Maxwell’s equations and Galilean invariance led Einstein to propose the special theory of relativity. Similarly, the inconsistency of special relativity with Newtonian gravity led him to develop the general theory of relativity. More recently, the reconciliation of special relativity with quantum mechanics led to the development of quantum field theory. We are now facing another crisis of the same character, namely general relativity appears to be incompatible with quantum field theory. Any straightforward attempt to ‘quantize’ general relativity leads to a nonrenormalizable theory. In my opinion, this means that the theory is inconsistent and needs to be modified at short distances or high energies. The way that string theory does this is to give up one of the basic assumptions of quantum field theory, the assumption that elementary particles are mathematical points, and instead to develop a quantum field theory of one-dimensional extended objects, called strings. There are very few consistent theories of this type, but superstring theory shows great promise as a unified quantum theory of all fundamental forces, including gravity. There is no realistic string theory of elementary particles that could serve as a new standard model, since there is much that is not yet understood. But that, together with a deeper understanding of cosmology, is the goal. This is still a work in progress. Even though string theory is not yet fully formulated, and we cannot yet give a detailed description of how the standard model of elementary particles should emerge at low energies, there are some general features of the theory that can be identified. These are features that seem to be quite generic irrespective of how various details are resolved. The first, and perhaps most important, is that general relativity is necessarily incorporated in the theory. It gets modified at very short distances/high energies but at ordinary distances and energies, it is present in exactly the form proposed by Einstein. This is significant, because it is arising within the framework of a consistent quantum theory. Ordinary quantum field theory does not allow gravity to exist; string theory requires it! The second general fact is that Yang–Mills gauge theories of the sort that comprise the standard model, naturally arise in string theory. We do not understand why the specific SU(3) × SU(2) × U(1) gauge theory of the standard model should be preferred, but (anomaly-free) theories of this general type do arise naturally at ordinary energies. The third general feature of string theory solutions is supersymmetry. The mathematical consistency of string theory depends crucially on supersymmetry, and it is very hard to find consistent solutions (quantum vacua) that do not preserve at least a portion of this supersymmetry. This prediction of string theory differs from the other two (general relativity and gauge theories) in that it really is a prediction. It is a generic feature of string theory that has not yet been discovered experimentally.