Ideas and Methods of Supersymmetry and Supergravity, or a Walk Through Superspace

Abstract

Preface. Mathematical background: The Poincar^D'e group, the Lorentz group Finite-dimensional representations of ^ISpin(3,1) The Lorentz algebra Two-component and four-component spinors Representations of the Poincar^D'e group Elements of differential geometry and gravity The conformal group The mass-shell field representation Elements of algebra with supernumbers Elements of analysis with supernumbers The supergroup of general coordinate transformations on R^Tp/q. Supersymmetry and superspace: Introduction: from R^Tp/q to supersymmetry Superalgebras, Grassmann-shells and super Lie groups The Poincar^D'e superalgebra Unitary representation of the Poincar^D'e superalgebra Real superspace R^T4/4 and superfields Complex superspace C^T4/2, chiral superfields and covariant derivatives The on-shell massive superfield representations The on-shell massless superfield representations From superfields to component fields The superconformal group. Field theory in superspace: Supersymmetric field theory Wess-Zumino model Supersymmetric nonlinear sigma-models Vector multiplet models Supersymmetric Yang-Mills theories Geometric approach to super Yang-Mills theories Classically equivalent theories. Quantized superfields: Picture-change operators Equivalence of component field and superfield perturbation theories Effective action (super) funtional The Wess-Zumino model: perturbative analysis Note about gauge theories Feynman rules for super Yang-Mills theories Renormalization Examples of counterterm calculations: an alternative technique Superfield effective potential. Superspace geometry of supergravity: Gauge group of supergravity and supergravity fields Superspace differential geometry Supergeometry with conformal supergravity constraints Prepotentials Einstein supergravity Prepotential de formations Supercurrent and supertrace Supergravity in components. Dynamics in supergravity: Pure supergravity dynamics Linearized supergravity Superg