Duality And Supersymmetric Theories

Essential reading for all mathematical physicists as a systematic book on this crucial subject.

The book begins with a brief review of supersymmetry, and the construction of the minimal supersymmetric standard model and approaches to supersymmetry breaking. General non-perturbative methods are also reviewed leading to the development of holomorphy and the Affleck-Dine-Seiberg superpotential as powerful tools for analysing supersymmetric theories. Seiberg duality is discussed in detail, with many example applications provided, with special attention paid to its use in understanding dynamical supersysmmetry breaking. The Seiberg-Witten theory of monopoles is introduced through the analysis of simpler N=1 analogues. Superconformal field theories are described along with the most recent development known as "amaximization". Supergravity theories are examined in 4, 10, and 11 dimensions, allowing for a discussion of anomaly and gaugino mediation, and setting the stage for the anti- de Sitter/conformal field theory correspondence. This book is unique in containing an overview of the important developments in supersymmetry since the publication of "Suppersymmetry and Supergravity" by Wess and Bagger. It also strives to cover topics that are of interest to both formal and phenomenological theorists.

This book reviews a number of spectacular advances that have been made in the study of supersymmetric quantum field theories in the last few years. Highlights include exact calculations of Wilson loop expectation values, and highly nontrivial quantitative checks of the long-standing electric-magnetic duality conjectures The book starts with an introductory article presenting a survey of recent advances, aimed at a wide audience with a background and interest in theoretical physics. The following articles are written for advanced students and researchers in quantum field theory, string theory and mathematical physics, our goal being to familiarize these readers with the forefront of current research. The topics covered include recent advances in the classification and vacuum structure of large families of N=2 supersymmetric field theories, followed by an extensive discussion of the localisation method, one of the most powerful tools for exact studies of supersymmetric field theories. The quantities that have been studied in this way are partition functions, expectation values of line operators, and supersymmetric indices. The book also reviews recently discovered connections between SUSY field theories in four dimensions and two-dimensional conformal field theory. These connections have a counterpart in relations between three-dimensional gauge theories and Chern-Simons theory; the book’s closing chapters explore connections with string theory.

In June 1997, fifty-seven of the world's best students gathered at TASI '97 in Boulder, Colorado, USA, to attend an intensive series of lectures on the theory and phenomenology of supersymmetry, supergravity and supercolliders. This book contains the proceedings of that school. It is aimed at advanced graduate students as well as postdoctoral and other researchers. It provides a snapshot of the state-of-the-art in an active area of high energy particle theory, and may perhaps serve as a preview of physics to be discovered in the next decade.

Understanding the dynamics of gauge theories is crucial, given the fact that all known interactions are based on the principle of local gauge symmetry. Beyond the perturbative regime, however, this is a notoriously difficult problem. Requiring invariance under supersymmetry turns out to be a suitable tool for analyzing supersymmetric gauge theories over a larger region of the space of parameters. Supersymmetric quantum field theories in four dimensions with extended N=2 supersymmetry are further constrained and have therefore been a fertile field of research in theoretical physics for quite some time. Moreover, there are far-reaching mathematical ramifications that have led to a successful dialogue with differential and algebraic geometry. These lecture notes aim to introduce students of modern theoretical physics to the fascinating developments in the understanding of N=2 supersymmetric gauge theories in a coherent fashion. Starting with a gentle introduction to electric-magnetic duality, the author guides readers through the key milestones in the field, which include the work of Seiberg and Witten, Nekrasov, Gaiotto and many others. As an advanced graduate level text, it assumes that readers have a working knowledge of supersymmetry including the formalism of superfields, as well as of quantum field theory techniques such as regularization, renormalization and anomalies. After his graduation from the University of Tokyo, Yuji Tachikawa worked at the Institute for Advanced Study, Princeton and the Kavli Institute for Physics and Mathematics of the Universe. Presently at the Department of Physics, University of Tokyo, Tachikawa is the author of several important papers in supersymmetric quantum field theories and string theory.

This is the proceedings of the third Nagoya workshop on Strong Coupling Gauge Theories (SCGT), after SCGT 88 and SCGT 90. As a tradition of the Nagoya SCGT workshops, the focus is on dynamical symmetry breaking with particular emphasis on the nontrivial fixed points and/or large anomalous dimension, which was actually the basis of walking technicolor, strong ETC technicolor and top quark condensate, etc. Special attention is also paid to the fixed point structure in supersymmetric gauge theories, which has recently been highlighted through duality arguments.

The contributions to this volume of the famous summer school in Les Houches cover the recent developments in supersymmetric string theory, the gauge theory/string theory correspondence and string duality. The book is a comprehensive introduction to the recent developments in string/M-theory and quantum gravity.

This book describes the basic concepts of supersymmetric theories. It is aimed at theorists, experimentalists and cosmologists interested in supersymmetry, and its content is correspondingly divided into three distinct tracks of study. The topics covered include a discussion of the motivation for supersymmetry in fundamental physics, a description of the minimal supersymmetric model as well as models of grand unification and string models, a presentation of the main scenarios forsupersymmetry breaking, including the concepts and results of dynamical breaking. On the astrophysics/cosmology side, the book includes discussions of supersymmetric dark matter candidates, inflation, dark energy, and the cosmological constant problem. Some very basic knowledge of quantum field theoryis needed and extensive appendices (in particular an introduction to the Standard Model of fundamental interactions) allow the reader to refresh and complete their notions.