Theories with Extra Dimensions

The motivation to invoke the existence of extra dimensions beyond the usual three spatial dimensions and one time dimension is to unify the forces of nature in a single framework. Phenomena which require very different explanations in four-dimensions (4D) can be shown to be manifestations of simpler theories in higher dimensions.

In the early 1900s the goal was to geometerize physics, i.e. to explain Nature as pure geometry. More concretely, it was hoped that matter in 4D could be explained as a manifestation of the curvature of a higher dimensional spacetime. Kaluza wrote a 5D version of General Relativity (GR) that contains Einstein's GR and Maxwell's Electromagnetism (EM), without the explicit introduction of matter into the theory. Thereby, he unified matter and geometry by showing that a photon in 4D was a manifestation of empty 5D spacetime. A limitation of Kaluza's work was that he assumed, without explanation, that the 5^th dimension does not affect the laws of physics. Klein subsequently proposed the idea of compactification as the physical basis for this assumption. If the extra dimension is circular with a radius smaller than 10^-15 mm, then the physical fields will depend on it periodically and the energies of the Fourier modes above the ground state would be so high as to be unobservable.

Once one attempts to incorporate the weak and strong forces into a higher-dimensional framework, the idea of "matter without matter", "charge without charge", and "geometry is everything" has to be abandoned. The reason is that it is not possible to find solutions to Einstein's equations without the explicit introduction of matter.

Kaluza-Klein (KK) theories have recently undergone an explosive revival. However, modern KK theories have significant differences from their ancestral counterparts. In the last decade it has been recognized that the tour de force of string theories (which are inherently higher-dimensional) is to obtain a framework that unifies gravity with the forces of the Standard Model. Many ideas arising in string theories have been applied to long-standing problems in particle physics with significant success. For example, a simple explanation of why the electroweak force is much stronger than the gravitational force can readily be obtained.

String theory consists of extended objects called branes on which all forces other than gravity can be confined. Since gravity is the dynamics of spacetime, it must propagate in all dimensions. If one considers a KK scenario in which gravity propagates in the 4+n dimensional bulk of spacetime with the electroweak and strong forces confined to a 3-brane (a 4D object which could be our Universe), then gravity appears to be a very weak force because the gravitational flux incident on the phase space occupied by our Universe (the brane) is extremely small. In fact, with the other forces confined to the brane, the size of the extra dimensions can be as large as millimeter, to be contrasted with a size of 10^-15 mm if all forces permeate the whole 4+n D bulk.

Such theories are appropriately called "Theories with Large Extra Dimensions". They have the profound consequence that gravity becomes strong at 10³ GeV, (rather than at 10¹⁸ GeV) and this energy is accessible at the coming generation of collider experiments. It is conceivable that quantum gravity effects may then be probed experimentally. Very interestingly, higher-dimensional black holes may be produced at colliders and be detected via their Hawking radiation.

Several contemporary problems of fundamental physics, like the cosmological constant problem and fermion-mass hierarchy problem, have also been addressed through the general principles of theories with large extra dimensions. In fact, one such theory does not even require that the extra dimension be compactified. The extra dimension could be infinitely large.

Phenomenology Institute researchers are actively involved in studies of these modern Kaluza-Klein theories. Our contributions range from the formulation of the low-energy effective theories to obtaining constraints on the sizes of these extra dimensions from precision measurements at colliders and from astrophysical measurements of the energy-loss rates in stars and supernovae. We have also investigated the cosmology and gauge-hierarchy arising from such theories.