##
**Introduction to superstrings.**
*(English)*
Zbl 0655.58001

Graduate Texts in Contemporary Physics. New York etc.: Springer-Verlag. xvi, 568 p. DM 98.00 (1988).

This book is organized in three parts. The first one (that includes the first five chapters) is a clear explanation of the basic ideas about string and superstring theories. It includes a review on path integrals and point particle theories. Strings and superstrings are introduced and first quantized in analogy with point particles. For superstrings, both the Neveu-Schwarz-Ramond (NS-R) model and the Green-Schwarz (G-S) model are discussed. In chapter 4, conformal field theory, combining the best features of NS-R and G-S formalisms, is investigated. Single loop and multiloop amplitudes are studied in chapter 5. This first part is a rather complete introduction. As a foundation for the developments of the theory, this part is essential for beginners and a valuable review for more advanced students.

The next two parts of the book introduce more advanced topics that are presently under research. Part II, composed of three chapters (6, 7 and 8), introduces string field theory. Initially the theory is discussed in the light cone formalism. Next, a fully covariant string theory is formulated with the introduction of Faddeev-Popov ghosts and BRST formalism. In chapter 8, string field theory is presented as the gauge theory of the universal string group (USG). Representations, connections and curvatures of the USG are derived. Advantages of this approach are discussed.

Part III deals with phenomenology. Chan-Paton factors and anomaly cancellation are used to fix the gauge group. Characteristic classes and Dirac index are studied to help the calculation of anomalies of the string theory. Chapter 10 is dedicated to the study of heterotic strings. It includes the spectrum of the theory, the covariant formulation and the calculation of single loop amplitudes. Lorentzian lattices are also discussed.

In the last chapter, the author studies compactification to four dimensions using Calabi-Yau spaces and orbifolds. Cohomology, homology, Kähler manifolds are reviewed. Symmetry breakdown of E(8) is discussed including the embedding of the spin connection, fermion generations and Wilson lines. These last two parts of the book are presented in a systematic and well organized style, making them a useful guide to further studies and research.

The next two parts of the book introduce more advanced topics that are presently under research. Part II, composed of three chapters (6, 7 and 8), introduces string field theory. Initially the theory is discussed in the light cone formalism. Next, a fully covariant string theory is formulated with the introduction of Faddeev-Popov ghosts and BRST formalism. In chapter 8, string field theory is presented as the gauge theory of the universal string group (USG). Representations, connections and curvatures of the USG are derived. Advantages of this approach are discussed.

Part III deals with phenomenology. Chan-Paton factors and anomaly cancellation are used to fix the gauge group. Characteristic classes and Dirac index are studied to help the calculation of anomalies of the string theory. Chapter 10 is dedicated to the study of heterotic strings. It includes the spectrum of the theory, the covariant formulation and the calculation of single loop amplitudes. Lorentzian lattices are also discussed.

In the last chapter, the author studies compactification to four dimensions using Calabi-Yau spaces and orbifolds. Cohomology, homology, Kähler manifolds are reviewed. Symmetry breakdown of E(8) is discussed including the embedding of the spin connection, fermion generations and Wilson lines. These last two parts of the book are presented in a systematic and well organized style, making them a useful guide to further studies and research.

Reviewer: V.Silveira

### MSC:

58Z05 | Applications of global analysis to the sciences |

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

81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |

81S40 | Path integrals in quantum mechanics |

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

17B67 | Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |

83E30 | String and superstring theories in gravitational theory |

58J20 | Index theory and related fixed-point theorems on manifolds |