String Theory and M-Theory

Gauge theory/string theory dualities 611
quantum mechanics breaks down when gravity is taken into account with
a resounding no, because the dual field theories are quantum theories with
unitary evolution.
q q
Fig. 12.1. A meson can be viewed as a quark and an antiquark held together by a
string.
The methods introduced in this chapter can be used to study the infrared
limits of various quantum field theories. Realistic models of QCD, for example,
should be able to explain confinement and chiral-symmetry breaking.
These properties are not present in models such as N = 4 super Yang–Mills
theory due to the large amount of unbroken supersymmetry. There is a variety
of ways to break these symmetries so as to get richer models, in both the
AdS/CFT and geometric transition approaches. In this setting, phenomena
such as confinement and chiral-symmetry breaking can be understood.
Matrix theory
With the discovery of the string dualities described in Chapter 8, it became
a challenge to understand M-theory beyond the leading D = 11 supergravity
approximation. Unlike ten-dimensional superstring theories, there is no
massless dilaton, and therefore there is no dimensionless coupling constant
on which to base a perturbation expansion. In short, 11-dimensional supergravity
is not renormalizable. Of course, ten-dimensional supergravity
theories are also not renormalizable, but superstring theory allows us to
do better. So one of the most fundamental goals of modern string theory
research is to understand better what M-theory is. An early success
was a quantum description of M-theory in a flat 11-dimensional space-time
background, called Matrix theory. This theory is discussed in Section 12.2.
Its fundamental degrees of freedom are D0-branes instead of strings. The
generalization to toroidal space-time backgrounds is also described. Matrix
theory is formulated in a noncovariant way, and it is difficult to use for explicit
computations, so the quest for a simpler formulation of Matrix theory
or a variant of it is an important goal of current string theory research.
Nevertheless, the theory is correct, and it has passed some rather nontrivial
tests that are described in Section 12.2.