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Mass Sum Rule of the Effective Action on Vacua with Broken Rigid N=1 Supersymmetry
We present an extension of the mass sum rule that applies to renormalizable
rigid supersymmetric field theories to the case of the N=1 supersymmetric
effective action (the gauged non-linear sigma model) consisting of adjoint
scalar superfields and vector superfields possessing a K"ahler potential, a set
of gauge coupling functions (second prepotential derivatives) and a
superpotential, which respectively set their energy scales. The mass sum rule
derived is valid for any vacua, including the (metastable) one of broken
supersymmetry with the condensates of D-term and/or F-term. We manage to extend
these analyses to the cases where superfields in (anti-)fundamental
representation are present. The supertrace is shown to vanish in those cases
where underlying geometry is special K"ahler and theory under concern is
anomaly free. Simple phenomenological application is given, providing an upper
bound for gaugino masses. We discuss that the effects of the D and/or F
condensates can be represented as a set of soft breaking terms with their
strengths predicted by the scales.Comment: 18 pages, no figure
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