By Francois Gieres
This monograph supplies a close and pedagogical account of the geometry of inflexible superspace and supersymmetric Yang-Mills theories. whereas the middle of the textual content is anxious with the classical thought, the quantization and anomaly challenge are in brief mentioned following a finished advent to BRS differential algebras and their box theoretical purposes. one of the taken care of subject matters are invariant varieties and vector fields on superspace, the matrix-representation of the super-Poincaré workforce, invariant connections on reductive homogeneous areas and the supermetric process. a number of facets of the topic are mentioned for the 1st time in textbook and are continuously provided in a unified geometric formalism. Requiring basically no historical past on supersymmetry and just a easy wisdom of differential geometry, this article will function a mathematically lucid advent to supersymmetric gauge theories.
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Additional info for Geometry of Supersymmetric Gauge Theories: Including an Introduction to BRS Differential Algebras and Anomalies
Example text
2 About formal gauge transformations In the following we briefly discuss the concept and characteristics of "formal gauge transformations" in ordinary space-time ; such transformations will be considered for the formulation of one of the constraints of SYM-theories. e. the corresponding gauge functions have different properties. 9 (iv) : the connection form ~a b representing locally on a manifold tion and the Christoffel symbols (r~)mn M a given linear connec- describing locally a corresponding covariant derivative are related by a formal gauge transformation given by the vielbein fields cam(x) (see eq.
Defines an irreducible representation of supersymmetry, namely the chiral superfield: Analogously, for the anti-chiral parametrization -~×? 84) ~)Note that for the natural coordinates (x,e,0) the "naive" constraint ~/~B~ ~(x,e,0) = 0 is not a supersymmetric one, since the linear operator ~/~0~ is not invariant under susy transformations. 85) and the differential constraint defines the anti-chiral superfield. With respect to the chiral parametrization the invariant frame takes (EAM) a "diagonal" form, 0 0 o and so does the corresponding superspace metric, .
22b) graded c y c l i c permutations of (A,B,C) Matter f i e l d s are described by m u l t i p l e t s of s u p e r f i e l d s definition depends on the representation chosen for tive of ~ A ; ¢. 1 whose p r e c i s e the YM-covariant deriva- is defined by (Here the group generators of the Lie algebra ~). 26b) for the ~-valued fields Q and the matter fields speaking the covariant derivatives ~DA ~ (Strictly respectively. are defined by their commutator being C but for the canonical linear connection these expressions obviously reduce ~M ~ to the previously given ones, if we write TAB ~ T[~=0]AB C.