Geometry of supersymmetric gauge theories : including an introduction to BRS differential algebras and anomalies / François Gieres

In this book the author gives a rather complete account of supersymmetric gauge theories in geometric language. There is an introduction to supersymmetry, including rigid supersymmetry generators, rigid superspace as a homogeneous space linear representation and the left and right actions. The author also discusses reductive homogeneous spaces, canonical structures and the Maurer-Cartan form. The first part is completed by the discussion of rigid superspace and Riemannian spaces, to be used in the description of N=1 super Yang-Mills theory (SYM).
The general structure of constraints in supersymmetric theories is discussed. SYM theory is discussed in the Wess-Zumino (WZ) gauge. The various representations are interconnected (gauge vector, chiral and antichiral). The problem of anomalies in general gauge theories is discussed in the BRS approach. From the Ward identities, the Wess-Zumino consistency condition is obtained, and presented as cohomology of the S-(BRS) operator.
This field approach is generalized to SYM theories in detail. The (field-dependent) field algebra in the WZ gauge is discussed. In the gauge vector representation, the supergeometry and mathematical structure of BRS are destroyed, it is claimed, due to field dependence of the algebra. The last part contains an account of extended (N>1) SYM theory. Constraints are discussed and integrability is mentioned.
The last appendix contains a fair account of the definition of anticommuting spinors in field theories. (MathScinet)