Lecture Notes in Physics Monograph Series: Volume m36
Springer-Verlag, Heidelberg, 1995
Self-dual Chern-Simons theories form a new class of self-dual gauge theories and provide a field theoretical formulation of anyonic excitations in planar (i.e. two space dimensional) systems. Chern-Simons gauge theories have attracted considerable attention recently in the particle physics, condensed matter physics and mathematical physics communities. Much of this attention is due to the surprising and novel ways in which such theories differ from the standard Maxwell, or Yang-Mills, gauge theories. These Chern-Simons theories are particular to planar systems and have therefore received added research impetus from recent experimental and theoretical breakthroughs in actual planar condensed matter systems such as the quantum Hall effect. These Lecture Notes give a pedagogical introduction to the basic properties of the special class of Chern-Simons theories known as ``self-dual'' Chern-Simons theories, concluding with an overview of more advanced results and an extensive bibliography. Such models possess Bogomol'nyi energy bounds, topological charges, vortex solutions and supersymmetric extensions, features which are familiar from other well-known self-dual systems such as instantons, monopoles and vortices. This book is intended mainly for graduate students having some familiarity with gauge theory, but will also be of interest to researchers in related fields.