Review of supersymmetry and supergravity

The general status and recent developments in the subjects of supersymmetry and supergravity are reviewed. At the global level, supersymmetry is the only invariance compatible with quantum field theory. Local supersymmetry is a gauge principle of a unique type, and automatically requires gravity. Therefore, the corresponding supergravity field theories link the concept of space-time geometry with the quantum mechanical notion of spin and statistics. There are still some difficulties. This report describes on some of the difficulties. The essential idea of supersymmetry is to construct quantum field theories with conserved spinor charges. There are Poincare, conformal, and DeSitter supersymmetries. Among three possible viewpoints, the algebraic view is discussed. A global supersymmetric theory is introduced. The basic supergravity theory is the gauge theory of the algebra. The locally supersymmetric field theory can be expressed as a minimal coupling Lagrangian using the Cartan-Palatini formalism of relativity. The proof of invariance of global and local supersymmetric field theories can be obtained by the direct calculation of the variation of Lagrangian using the appropriate field transformation laws. There are the unified supergravity, the matter coupling, and the conformal supergravity theories. The general properties and status of these theories are discussed. Selected recent work in global supersymmetry and selected recent work in supergravity are presented. (Kato, T.)