String Theory and M-Theory

Flux compactifications 459
Some models are known in which all moduli are fixed, and a supergravity
approximation still can be justified. In these models the fluxes take integer
values N, which can be arbitrarily large in such a way that the supergravity
description is valid in the large N limit.
The string theory landscape
Even though flux compactifications can stabilize the moduli fields appearing
in string theory compactifications, there is another troubling issue. Flux
compactifications typically give very many possible vacua, since the fluxes
can take many different discrete values, and there is no known criterion for
choosing among them. These vacua can be regarded as extrema of some potential,
which describes the string theory landscape. Section 10.6 discusses
one approach to addressing this problem, which is to accept the large degeneracy
and to characterize certain general features of typical vacua using
a statistical approach.
Fluxes and dual gauge theories
Chapter 12 shows that superstring theories in certain backgrounds, which
typically involve nonzero fluxes, have a dual gauge-theory description. The
simplest examples involve conformally invariant gauge theories. However,
there are also models that provide dual supergravity descriptions of confining
supersymmetric gauge theories. Section 10.2 describes a flux model that is
dual to a confining gauge theory in the context of the type IIB theory, the
Klebanov–Strassler (KS) model. The dual gauge theory aspects of this model
are discussed in Chapter 12.
Brane-world scenarios
An alternative to the usual Kaluza–Klein compactification method of hiding
extra dimensions, called the brane-world scenario, is described in Section
10.2. One of the goals of this approach is to solve the gauge hierarchy problem,
that is, to explain why gravity is so much weaker than the other forces.
The basic idea is that the visible Universe is a 3-brane, on which the standard
model fields are confined, embedded in a higher dimension space-time.
Extra dimensions have yet to be observed experimentally, of course, but in
this set-up it is not out of the question that this could be possible. 3 While
3 The search for extra dimensions is one of the goals of the Large Hadron Collider (LHC) at
CERN, which is scheduled to start operating in 2007.