String Theory and Extra Dimensions

It is a common belief held by many theorists that our physical world is not limited to just four dimensions (one time plus three space dimensions), but it can actually extend to as many as eleven dimensions (one time plus ten space dimensions). The revolutionary idea of extra dimensions was proposed independently by Kaluza (1921) and Klein (1926) in an attempt to unify electromagnetism with general relativity. It has since been an important ingredient of superstring theory which tries to unify the four types of fundamental interactions. In the Kaluza-Klein theory, the extra spatial dimensions are assumed to be "compactified", in other words, they curl up on such a small scale that they have no physical consequence to low-energy physics. This small scale is usually identified with the fundamental string scale, far away from the electroweak scale which is now being probed.

However, recent advances in superstring theory suggest that the string or compactification scale can be substantially lower. A bold recent proposal suggests that the string scale is at the TeV scale; this corresponds to extra dimensions of millimeter size. To evade present experiment bounds, the Standard Model fields should live on a four-dimensional subspace. There are many experimental consequences for this new proposal. First, since gravity propagates in the millimeter-size extra dimensions, precise table-top experiments should find deviations from Newton's law. Second, although the Standard Model fields do not feel the extra dimensions directly, they couple to some remnants of the extra dimensions called Kaluza-Klein states. Future experiments should be able to observe effects due to these states if the string scale is as low as a TeV. Finally, these Kaluza-Klein states have many cosmological and astrophysical implications.

We have formulated the effective theory of Kaluza-Klein graviton and matter interactions; this work has been the foundation of recent phenomenological studies of the TeV gravity theory. Many interesting processes involving Kaluza-Klein gravitons are being examined. We obtained constraints on the string scale from energy-loss processes of the hot astrophysical objects like the sun, red giants and supernovae, and from electroweak precision measurements.