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Preface to the 25th Anniversary Edition

In the twenty-five years since the original publication of these two
Volumes, there have been numerous developments in string theory. The
curious twists and turns that marked its pre-1987 evolution have continued
apace, and current research makes contact with a wide range of areas of
mathematics and physics. In the following we will mention briefly some of
these developments and then explain why we believe that these volumes
are still useful.

Major insights into the non-perturbative structure of string theory
followed from the discovery of non-perturbative duality symmetries of
super-string theory. This led to the realization that the myriad of apparently
distinct superstring theories that arise in ten or fewer dimensions actually
are different perturbative approximations to the same underlying theory,
which has come to be known as M-theory. Furthermore, M-theory has
eleven-dimensional supergravity as another semiclassical limit. The
understanding of these interconnections was aided by the simultaneous
discovery of the properties of a family of dynamical objects called p-branes,
which are extended objects that fill p spatial dimensions, as opposed to
the 1 dimension of the string. p-branes can be viewed as solitons that are
generalizations of the magnetic monopoles of conventional quantum field
theory and the black holes of general relativity. Indeed, these discoveries
have stimulated impressive advances in understanding the quantum and
thermodynamic properties of large classes of black holes.

An important outcome of these considerations has been striking
progress in understanding the nonperturbative structure of the quantum
field theories that arise from string theory in various limits. Most notably,
it has led to the gauge/gravity correspondence, also known as holographic
duality, according to which a quantum theory of gravity in a D-dimensional
asymptotically anti-de Sitter spacetime is equivalent to a (D — l)-
dimensional local quantum field theory. The most studied example is an
equivalence between four-dimensional maximally supersymmetric U(N)
Yang–Mills field theory and type IIB superstring theory in five-dimensional
anti-de Sitter space times a five-dimensional sphere with N units of
Ramond–Ramond flux.

In 1987, the main focus of this field was the application of string
perturbation theory to describe the fundamental forces and particles. This
remains a focus, but nowadays nonperturbative methods are used as well.
The possibilities for using string theory to construct models of particle
physics that are at least semi-realistic have proliferated since 1987,
and some physicists, in part because of clues coming from cosmological
observations, have come to suspect that the “landscape” of string theory
possibilities is actually the way the Universe works. In addition, nowadays,
string theory is applied to other types of problems in theoretical physics,
including the modeling of heavy ion collisions and the theory of quantum
critical points relevant to condensed matter physics. From a contemporary
point of view, the gauge/gravity correspondence means that string theory
and quantum gravity are inevitable parts of the description of strongly
coupled quantum systems.

Many of the developments of the last quarter century, which of course
are not covered in these two volumes, have been described in more recent
books and review articles. These more recent developments are rooted to a
large extent in the basic material covered here. Given the immense breadth
and volume of recent research, it is extremely difficult for newer books and
articles to present all the details of the more basic underlying material. For
this reason, we feel that the material contained in these volumes remains of
value and we hope it will continue to provide stimulus for further research
in this rich field – wherever it eventually may lead.

Michael B. Green
John H. Schwarz
Edward Witten

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