## Geometry of Supersymmetric Gauge Theories: Including an Introduction to Brs Differential Algebras and AnomaliesThis monograph gives a detailed and pedagogical account of the geometry of rigid superspace and supersymmetric Yang-Mills theories. While the core of the text is concerned with the classical theory, the quantization and anomaly problem are briefly discussed following a comprehensive introduction to BRS differential algebras and their field theoretical applications. Among the treated topics are invariant forms and vector fields on superspace, the matrix-representation of the super-PoincarA(c) group, invariant connections on reductive homogeneous spaces and the supermetric approach. Various aspects of the subject are discussed for the first time in textbook and are consistently presented in a unified geometric formalism. Requiring essentially no background on supersymmetry and only a basic knowledge of differential geometry, this text will serve as a mathematically lucid introduction to supersymmetric gauge theories. |

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### Contents

PREFACE | 1 |

THE GENERAL STRUCTURE OF SYMTHEORIES | 46 |

CLASSICAL SYMTHEORIES IN THE GAUGE REAL REPRESENTATION | 79 |

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anomaly anti-chiral anticommuting antiderivation antisymmetric approach Bianchi identities BRS algebra BRS differential algebra canonical linear connection chiral basis chiral representation chiral superfield cohomology component field algebra consider constraints corresponding covariant derivatives curvature defined definition denote differential algebra equations equivalent expression fermionic field algebra field dependent Field Theory formal gauge transformation gauge covariant derivatives gauge field gauge theory gauge transformation geometric ghost number given Grassmann hermitean conjugation infinitesimal introduce invariant Lagrangian left-invariant Lett Lie algebra valued Lie G Lie group linear connection manifold mathematical Maurer-Cartan metric Minkowski space multiplet nilpotent Nucl operator parameter Phys prepotential quantization quantum real representation reality condition relations represents resp Riemannian rigid superspace s-variation satisfies solution SP/L spinor Stora structure super superconnection supergauge transformations supergravity supersymmetry susy algebra susy transformations SYM-theories symmetry tensor transformation law variables vector field vector space vielbein forms WZ-gauge