Modern Supersymmetry, Dynamics and Duality

Abstract

Since its proposition over 35 years ago, supersymmetry has been the focus of intense investigation in both theoreticaland particle physics. There are many excellent textbooks in the literature which give an introduction to the 'traditional' topics of supersymmetry like the supersymmetry algebra, superfields, supersymmetric gauge theories and supergravity.In recent years our understanding of non-perturbative phenomena in supersymmetric gauge theories has undergone somethingof a revolution with the use of non-renormalization theorems, duality and holomorphy. These powerful techniques have given new insights into vacuum structure, confinement and strong coupling behaviour of some gauge theories.Non-renormalization theorems in supersymmetric theories have been known for some time. These state that, under some conditions, certain terms of supersymmetric actions are not renormalized in the quantum theory.These include for example the potential term in the Wess–Zumino model and the ultra-violet finiteness of N = 4 supersymmetric gauge theory in four dimensions. The original proof of these theorems was given using light-cone techniques, supergraph methods and anomaly arguments. More recently, non-renormalization theorems have been shown using holomorphy.In many cases, the interaction terms of supersymmetric theories depend holomorphically on chiral superfields and some coupling constants. In addition, these interaction terms are invariant under transformations that act both on the coupling constants and on the fields. Holomorphy is the assertion that after quantum corrections are taken into account, the above interaction terms remain holomorphic in the way suggested above and invariant under the transformations that act on the fields and couplings. This leads to strong restrictions on the type of effective potentials that can occur. In turn, it gives insights into the vacuum structure of gauge theories. Some time ago, it was observed by Montonen and Olive that mass formulae for particle states and magnetic monopoles in gauge theories are invariant under the exchange of particles and magnetic monopoles and the simultaneous inversion of a coupling constant. A consequence of this is that it makes a prediction about the light states of gauge theories at strong coupling. In the last ten years, this paradigm has been extensively investigated and generalized.This book combines the traditional material on supersymmetric gauge theories with the more recent developments on duality and holomorphy. It is the first time that a description of these works on supersymmetry has appeared in book form. The author has made a good selection of topics from a vast literature of research papers and review articles. He has presented the material in a way that leads the reader from the origins to the advanced areas of the field. In particular, the supersymmetric standard model is described. Then holomorphy, Seiberg duality, dynamical supersymmetry breaking and the Seiberg–Witten theory are presented. The book finishes with an outline of the AdS/CFT correspondence.To read the book a good knowledge of quantum field theory and some previous familiarity with supersymmetry are required. The timing for this book could not have been more appropriate. There is much expectation that supersymmetry could be discovered at LHC, CERN.The practitioners of supersymmetry will enjoy reading this book.It will also be an invaluable guide to those who wish to venture onto the landscape of the non-perturbative aspects of supersymmetric gauge theories.