Considerations of the sort we encountered in the previous chapter have inspired two approaches to physics beyond the Standard Model: large extra dimensions (ADD) and warped spaces (Randall–Sundrum). In this chapter we will provide a brief introduction to each.

Large extra dimensions: the ADD proposal

In string theory, it is natural to imagine that the compactification scale is not too much different from the Planck scale. The size of the compact space is typically a modulus, and if it is stabilized, one might expect it be stabilized at a value not much different than one, in string (and therefore Planck) units. In terms of our general discussion of moduli stabilization, this is precisely what we would expect: once the radius becomes very large, any potential, perturbative or non-perturbative, tends to zero.

But if we are willing to discard this prejudice, an extraordinary possibility opens up. Perhaps the extra dimensions are not Planck size, but much larger, even macroscopic? Arkani-Hamed, Dimopoulos and Dvali realized that from an experimental point of view, the limits on the size of such large compact dimensions are surprisingly weak. Allowing the extra dimensions to be large totally reorients our thinking about the nature of couplings and scales in string theory (or any underlying fundamental theory). Such a viewpoint places the hierarchy problem in a whole different light, perhaps allowing entirely different solutions than technicolor or supersymmetry.

Branes are crucial to this picture. The observed gauge couplings are small, but not extremely small. But in Kaluza–Klein theory and in weakly coupled string theories, they are related to the underlying scales in a clear way.