String Theory - Basic Properties

Basic Properties

String theory can be formulated in terms of an action principle, either the Nambu-Goto action or the Polyakov action, which describe how strings propagate through space and time. In the absence of external interactions, string dynamics are governed by tension and kinetic energy, which combine to produce oscillations. The quantum mechanics of strings implies these oscillations exist in discrete vibrational modes, the spectrum of the theory.

On distance scales larger than the string radius, each oscillation mode behaves as a different species of particle, with its mass, spin and charge determined by the string's dynamics. Splitting and recombination of strings correspond to particle emission and absorption, giving rise to the interactions between particles. An analogy for strings' modes of vibration is a guitar string's production of multiple distinct musical notes. In the analogy, different notes correspond to different particles. One difference is the guitar string exists in 3 dimensions, so that there are only two dimensions transverse to the string. Fundamental strings exist in 9 dimensions and the strings can vibrate in any direction, meaning that the spectrum of vibrational modes is much richer.

String theory includes both open strings, which have two distinct endpoints, and closed strings making a complete loop. The two types of string behave in slightly different ways, yielding two different spectra. For example, in most string theories one of the closed string modes is the graviton, and one of the open string modes is the photon. Because the two ends of an open string can always meet and connect, forming a closed string, there are no string theories without closed strings.

The earliest string model, the bosonic string, incorporated only bosonic degrees of freedom. This model describes, in low enough energies, a quantum gravity theory, which also includes (if open strings are incorporated as well) gauge fields such as the photon (or, in more general terms, any gauge theory). However, this model has problems. What is most significant is that the theory has a fundamental instability, believed to result in the decay (at least partially) of spacetime itself. In addition, as the name implies, the spectrum of particles contains only bosons, particles which, like the photon, obey particular rules of behavior. In broad terms, bosons are the constituents of radiation, but not of matter, which is made of fermions. Investigating how a string theory may include fermions in its spectrum led to the invention of supersymmetry, a mathematical relation between bosons and fermions. String theories that include fermionic vibrations are now known as superstring theories; several kinds have been described, but all are now thought to be different limits of M-theory.

Some qualitative properties of quantum strings can be understood in a fairly simple fashion. For example, quantum strings have tension, much like regular strings made of twine; this tension is considered a fundamental parameter of the theory. The tension of a quantum string is closely related to its size. Consider a closed loop of string, left to move through space without external forces. Its tension will tend to contract it into a smaller and smaller loop. Classical intuition suggests that it might shrink to a single point, but this would violate Heisenberg's uncertainty principle. The characteristic size of the string loop will be a balance between the tension force, acting to make it small, and the uncertainty effect, which keeps it "stretched". As a consequence, the minimum size of a string is related to the string tension.