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Supersymmetric Yang-Mills theories with local coupling: The supersymmetric gauge
Supersymmetric pure Yang-Mills theory is formulated with a local, i.e.
space-time dependent, complex coupling in superspace. Super-Yang-Mills theories
with local coupling have an anomaly, which has been first investigated in the
Wess-Zumino gauge and there identified as an anomaly of supersymmetry. In a
manifest supersymmetric formulation the anomaly appears in two other
identities: The first one describes the non-renormalization of the topological
term, the second relates the renormalization of the gauge coupling to the
renormalization of the complex supercoupling. Only one of the two identities
can be maintained in perturbation theory. We discuss the two versions and
derive the respective beta function of the local supercoupling, which is
non-holomorphic in the first version, but directly related to the coupling
renormalization, and holomorphic in the second version, but has a non-trivial,
i.e.anomalous, relation to the beta function of the gauge coupling.Comment: References correcte
The Antighost Equation in N=1 Super-Yang-Mills Theories
The antighost equation valid for usual gauge theories in the Landau gauge, is
generalized to the case of supersymmetric gauge theories in a
supersymmetric version of the Landau gauge. This equation, which expresses the
nonrenormalization of the Faddeev-Popov ghost field, plays an important role in
the proof of the nonrenormalization theorems for the chiral anomalies.Comment: 8 pages, for the sake of clarity expressions (3.1) and (3.2) have
been modified. Due to an E-mail error, the old file was empt
Algebraic Renormalization of Supersymmetric Gauge Theories with Supersymmetry Breaking Masses
We provide N=1 Super Yang-Mills theory in the Wess-Zumino gauge with mass
terms for the supersymmetric partners of the gauge fields and of the matter
fields, together with a supersymmetric mass term for the fermionic matter
fields. All mass terms are chosen in such a way to induce soft supersymmetry
breakings at most, while preserving gauge invariance to all orders of
perturbation theory. The breakings are controlled through an extended
Slavnov-Taylor identity. The renormalization analysis, both in the ultraviolet
and in the infrared region, is performed.Comment: 24 pages, plain LaTeX, no figure
Supersymmetry algebra cohomology III: Primitive elements in four and five dimensions
The primitive elements of the supersymmetry algebra cohomology as defined in
a previous paper are computed for standard supersymmetry algebras in four and
five dimensions, for all signatures of the metric and any number of
supersymmetries.Comment: v2: D=4 analysis simplified, D=5 analysis added, refs. added, typos
corrected, 32 page
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