M-theory and string duality

During the “Second Superstring Revolution,” which took place in the mid- 1990s, it became evident that the five different ten-dimensional superstring theories are related through an intricate web of dualities. In addition to the T-dualities that were discussed in Chapter 6, there are also S-dualities that relate various string theories at strong coupling to a corresponding dual description at weak coupling. Moreover, two of the superstring theories (the type IIA superstring and the E 8 × E 8 heterotic string) exhibit an eleventh dimension at strong coupling and thus approach a common 11-dimensional limit, a theory called M-theory . In the decompactification limit, this 11-dimensional theory does not contain any strings, so it is not a string theory. Low-energy effective actions This chapter presents several aspects of M -theory, including its low-energy limit, which is 11-dimensional supergravity, as well as various nonperturbative string dualities. Some of these dualities can be illustrated using low-energy effective actions. These are supergravity theories that describe interactions of the massless fields in the string-theory spectrum. It is not obvious, a priori , that this should be a useful approach for analyzing nonperturbative features of string theory, since extrapolations from weak coupling to strong coupling are ordinarily beyond control. However, if one restricts such extrapolations to quantities that are protected by supersymmetry, one can learn a surprising amount in this way.