# String theory

String theory is a big subject. Here's a brief introduction; for more, try Patricia Schwarz's string theory page or the Cambridge relativity group's string page.

The basic idea of string theory is to replace point particles with "strings," one-dimensional objects that can come as loops (closed strings) or segments (open strings). This gives a very rich structure -- string theories typically involve more than four spacetime dimensions, and strings can both vibrate and "wrap around" extra compact dimensions, leading to an enormous number of possible quantum states. The hope is that these states can unify gravity and elementary particle physics into a single framework, and that, if we are extremely lucky, only one self-consistent theory will exist.

Gravity comes into string theory in two closely related ways. First, one of the states of a closed string is a "graviton," a massless, self-interacting spin two particle. There are general results that any theory describing such a particle has to look like general relativity at low energies. Second, if one looks at a string propagating in a curved spacetime background, one finds that a consistent description is only possible if the background obeys certain restrictions, which again look like the Einstein field equations at low energies. These two results seem independent, but they are actually linked -- the consistent background in which strings can propagate can be described as a quantum state (technically, a "coherent state") of string excitations, including gravitons.

For many years, it looked as if there were several distinct self-consistent string theories. But the "duality revolution" of the 1990s showed that they all seem to be related by a set of duality transformations, which typically relate the strongly-coupled behavior of one string theory with the weakly-coupled behavior of another. This development has given us a glimpse of a larger landscape, in which the string theories we know are only small pieces. The hypothetical big picture is called M theory (M for "mystery," "matrix," "membrane," and a number of other possibilities). We don't know much about M theory as a whole, though we do know that it is not only a theory of strings -- higher-dimensional objects, membranes or "branes" for short, also play essential roles. A further revolution has come with the AdS/CFT correspondence, a remarkable relation between string theory, including gravity, in certain spacetimes ("asymptotically anti-de Sitter spaces") and lower dimensional conformal field theories that don't include gravity.

String theory has shown enough striking coincidences -- surprising internal consistencies that have even led to deep new results in mathematics -- that most practitioners are convinced that a deep underlying structure exists. But we don't yet know what that structure is. Ed Witten, for example, has said that the one of the most fundamental questions in string theory is to understand "what is the new kind of geometry that generalises what Einstein used." We also don't know, in a practical sense, how unique string theory is: even if there is only one consistent theory, there seem to be an extraordinarily large number of "ground states," each of which gives not only a different spacetime geometry, but a different particle content and a different gauge group for elementary particles. Whether one of these states describes the real Universe, and, if so, whether there is any way to pick it out as being special, remains to be seen.

String theory is also just now beginning to address some of the general conceptual problems of quantum gravity: the problem of finding local observables to describe spacetime, for example, and the question of what quantum gravity does about singularities. Most of what we can actually do in string theory involves perturbation theory around a fixed classical background, a process that postpones these deep issues but cannot entirely remove them.

### Contributors

- Steve Carlip (Physics, UC Davis)