Geometry of supersymmetric gauge theories. Including an introduction to BRS differential algebras and anomalies
Systematic and selfcontained account of the geometric formulation of supersymmetric Yang-Mills theories is given. The first chapter deals with the geometric structure of superspace. The concept of superspace is introduced in the standard way as the quotient space SP/L, where SP is the super-Poincaré group and L is the Lorentz one. The action of supersymmetry transformations is defined and the left- invariant vector fields (``SUSY covariant derivatives'') and forms on superspace are constructed. The linear representation of S-P group in terms of \(9\times 9\) matrices is then given and used to calculate the Maurer-Cartan forms on S-P group and their pullbacks to superspace. Using the Wang theorem concerning the classification of connections on homogeneous spaces it is shown how the geometry of superspace can be interpreted from the point of view of general theory. Finally, the relation to the Riemannian approach due to P. P. Srivastava and G. Woo is described. The second and third chapters deal with the supersymmetric Yang-Mills theories (SYM). The geometric framework of SYM is presented. The real and chiral/anti-chiral representations are separately discussed. Fourth chapter is devoted to the study of BRS symmetry. BRS symmetry is formulated in terms of differential algebra. As an application the problem of determining the structure of anomalies is carefully discussed. Further, the BRS algebra and anomalies in SYM theories are discussed. Finally, the author's geometric approach to the BRS algebra is presented. The book is supplied with several appendices and carefully selected list of references. It provides a valuable introduction to the geometric approach to SYM. In particular, the chapter devoted to the BRS symmetry is very useful.
scientific article; zbMATH DE number 193200