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**String theory and M-theory: a modern introduction.**
*(English)*
Zbl 1123.81001

Cambridge: Cambridge University Press (ISBN 978-0-521-86069-7/hbk; 978-0-511-25486-4/ebook). xvi, 739 p. (2007).

String theory has a long history starting with the Nambu-Goto action, the Virasoro algebra and its central extension with the critical dimension 26. Modern string theory began with the discovery of superstrings (1984) living in ten dimensions. M-theory – often referred to as Matrix theory – living in eleven dimensions explains how five different superstring theories, connected by dualities, can be united.

There are three distinguished books on string theory preceding this one, written by M. B. Green, J. H. Schwarz and E. Witten [Superstring theory. Volume 1: Introduction. Volume 2: Loop amplitudes, anomalies and phenomenology. Cambridge Monographs on Mathematical Physics (1987; Zbl 0619.53002)], by J. Polchinski [String theory. Volume I: An introduction to the bosonic string. Volume II: Superstring theory and beyond. Cambridge Monographs on Mathematical Physics (1998; Zbl 1006.81521 and Zbl 1006.81522)], and by B. Zwiebach [A first course in string theory (2004; Zbl 1072.81001)]. All were published as this one by Cambridge University Press. Naturally, each of the four books claims to be more up-to-date than the preceding ones. This however is made possible only by concentrating on selected topics of current research, while previous books admittingly contain material, often valuable, that is no longer repeated. Even today string theory and M-theory need certain spacetime backgrounds and thus are often subject to criticism. For they do not seem to provide a quantum version of general relativity as intended.

However, a critical assessment is not the subject of the present book. It rather tries to lead graduate students as well as researchers to the frontiers of modern research. The curious reader may ask: what after all is M-theory? Here the answer is rather vague. Though there are many known M-theory vacua, there is as yet no convincing formulation of an underlying theory. Also, one only expect a vacuum to exist that belongs to our known world of particle physics.

In any case the reader is assumed to be familiar with quantum field theory, general relativity and on the mathematical side with differential geometry, algebraic topology and group theory though the emphasis of the book is not on abstract mathematics. There is a large bibliography which is very helpful. Another important feature of the book is that it offers many exercises with worked-out solutions.

There are three distinguished books on string theory preceding this one, written by M. B. Green, J. H. Schwarz and E. Witten [Superstring theory. Volume 1: Introduction. Volume 2: Loop amplitudes, anomalies and phenomenology. Cambridge Monographs on Mathematical Physics (1987; Zbl 0619.53002)], by J. Polchinski [String theory. Volume I: An introduction to the bosonic string. Volume II: Superstring theory and beyond. Cambridge Monographs on Mathematical Physics (1998; Zbl 1006.81521 and Zbl 1006.81522)], and by B. Zwiebach [A first course in string theory (2004; Zbl 1072.81001)]. All were published as this one by Cambridge University Press. Naturally, each of the four books claims to be more up-to-date than the preceding ones. This however is made possible only by concentrating on selected topics of current research, while previous books admittingly contain material, often valuable, that is no longer repeated. Even today string theory and M-theory need certain spacetime backgrounds and thus are often subject to criticism. For they do not seem to provide a quantum version of general relativity as intended.

However, a critical assessment is not the subject of the present book. It rather tries to lead graduate students as well as researchers to the frontiers of modern research. The curious reader may ask: what after all is M-theory? Here the answer is rather vague. Though there are many known M-theory vacua, there is as yet no convincing formulation of an underlying theory. Also, one only expect a vacuum to exist that belongs to our known world of particle physics.

In any case the reader is assumed to be familiar with quantum field theory, general relativity and on the mathematical side with differential geometry, algebraic topology and group theory though the emphasis of the book is not on abstract mathematics. There is a large bibliography which is very helpful. Another important feature of the book is that it offers many exercises with worked-out solutions.

Reviewer: Gert Roepstorff (Aachen)

### MSC:

81-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory |

81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |

83E30 | String and superstring theories in gravitational theory |

83E50 | Supergravity |

81T60 | Supersymmetric field theories in quantum mechanics |

83-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to relativity and gravitational theory |