# Quantum Chromodynamics: Perturbative and Nonperturbative Aspects

28 September 2010

by Boris L Ioffe, Victor S Fadin and Lev N Lipatov, Cambridge University Press. Hardback ISBN 9780521631488, £110.00 ($180). E-book ISBN 9780511717444$144.

The latest addition to the large library of books devoted to the strong interaction, Quantum Chromodynamics: Perturbative and Nonperturbative Aspects, is a long awaited gem. For a long time I witnessed the efforts of one of the editors, Peter Landshoff, waiting for the manuscript finally to come to life. The authors, Boris Ioffe, Victor Fadin and Lev Lipatov, are outstanding theoretical physicists and true masters in the field. They have made crucial contributions to a theory that, despite Titanic efforts, has kept its most intimate mysteries as secret as in its childhood days.

Before highlighting its content, it is fair to say that this is not an easy book to read; it is more of a wise companion to work with. There is a clear intention to present the results from first principles, departing from other more “user friendly” textbooks. There are numerous references to research papers to help the reader reach a deep understanding of the discussions presented in the text. The underlying spirit is that learning must follow from full control of the technical details, leaving analogies and “pretty pictures” for “amateurs”.

In almost 600 pages, the authors have been able to cover only selected topics in line with their research interests. The final result, a collage of perturbative and nonperturbative aspects of the theory, is nevertheless attractive. In many newspapers there are weekly columns dedicated to reviews of the best moves of famous chess games: the final results are known but we are still delighted with the details of certain moves. Let us follow this philosophy and comment on the most remarkable “games” in this book.

It begins by introducing quantization, with a lucid discussion of the Gribov ambiguity and renormalization schemes. It continues with the spontaneous violation of chiral symmetry and introduces chiral-effective theories at low energies. The axial and scale anomalies are then presented with care. The nontrivial structure of the QCD vacuum is also explored, first introducing tunnelling in quantum mechanics, followed by a superb description of instantons and topological currents. To illustrate the divergent nature of quantum field theory, the authors provide many examples on how to estimate higher-order corrections ranging from renormalons to functional approaches – this is highly recommendable. QCD sum rules are then explained in detail, together with a nice discussion on the determination of the running of the strong coupling and condensates from low-energy data. Different meson and baryon properties are derived in depth.

When the perturbative window is opened, the evolution equations in the parton model take central stage. The presentation here is very original, full of useful intermediate steps and dealing with less well known subjects such as parton-number correlators. Parton distributions for unpolarized and polarized nucleon targets, quasipartonic operators and infrared evolution equations at small Bjorken x are included in the menu. Jet production, starting with e+e annihilation into hadrons, also appears. I recommend that the reader pay special attention to the sections devoted to colour coherence.

The last two chapters are closest to my heart: the Balitsky-Fadin-Kuraev-Lipatov (BFKL) approach and high-energy QCD. This subject attracted a great deal of attention in physics at the HERA collider at DESY, and is returning in a rather unexpected way: the anti de Sitter/conformal-field theory (AdS/CFT) correspondence. The original derivation of the BFKL equation, including the next-to-leading-order kernel, is presented. Special emphasis is put on using the dominant degrees of freedom at high energies, the reggeized gluons and the solid bootstrap conditions that they fulfil. The book closes with a presentation of an effective action to describe reggeized gluon interaction, the appearance of integrability, the current view of the hard pomeron in supersymmetric theories and its connection to graviton exchange in dual theories. This line of research has a bright future, but this will be the subject for other books. For the time being, remember to keep this one, not at your bedside, but on your work table.