Mathematics – Logic
Scientific paper
Jun 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008cqgra..25l9001.&link_type=abstract
Classical and Quantum Gravity, Volume 25, Issue 12, pp. 129001 (2008).
Mathematics
Logic
Scientific paper
This volume presents a comprehensive introduction to supersymmetry, concentrating mainly on the Minimal Supersymmetric Standard Model (MSSM) and its possible embedding in a grand unified theory, but also including material on supergravity, non-perturbative aspects of supersymmetry, string theory and cosmology. There is an excellent self-contained appendix on the standard model which could be read first; other appendices provide introductions to spinor representations of the Lorentz group, superfields, and cosmology, and there is a short appendix listing the MSSM renormalisation group beta-functions. The appendices in fact occupy over a quarter of the volume. Substantial knowledge of quantum field theory is required of the reader; and also a working knowledge of group theory as employed in the construction of particle physics models: while there is some useful material on this in the section on grand unification, an appendix on it might perhaps have been a useful addition.
Supersymmetry is introduced via the particle physicist's concern with the hierarchy problem and developed in the component formalism beginning with the Wess Zumino model and proceeding to supersymmetric gauge theories. The treatment is detailed and authoritative; the author has 25 years of high-level research experience in the area and it shows. The level of presentation is high, and difficult concepts are explained clearly. The examples and associated hints are excellent. One topic I would have liked to see more on is the renormalisation of supersymmetric theories; presentation of the explicit calculation of the anomalous dimension of a chiral superfield (gamma) at one loop for at least the Wess Zumino model might perhaps have been pedagogically useful. Associated, perhaps, with this omission is an inconsistency in the definition of gamma; the sign of gamma in the treatment in section 8.3.2 clearly differs from its sign in the appendix section E.3.
In the text the formalism of supersymmetry is developed mainly in terms of four-component Majorana spinors, while use of two-component spinors is relegated to the appendices, where the author valiantly presents results in a manner facilitating translation between different conventions, which is very useful. In the main text, however, the reader might even be led to feel that the Wess Zumino model actions for a Majorana fermion on the one hand and a chiral fermion on the other are different theories, whereas in fact one can of course be rewritten as the other. I feel that the two-component formalism could have been profitably introduced at an earlier stage and used more consistently.
The book concludes with discussions of two 'challenges' to supersymmetry, as presented by the flavour problem and the cosmological constant. These are full of interesting and (indeed) challenging material, at the frontier of present-day research.
This is an excellent and up-to-date book, and very timely vis-à-vis the Large Hadron Collider. It would make an excellent graduate text for graduate students in particle theory. 'Road-maps' for high energy experimentalists and cosmologists are also provided; however for experimentalists a text with more in the way of, for example, explicit calculations of cross-sections would probably be more useful.
To summarise: minor quibbles aside, a fine book with a wealth of exciting material, and to be thoroughly recommended to any theoretically-inclined graduate student who has done a field theory course and wants to really get to grips with any aspect of supersymmetry.
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