Some Explorations in Holomorphy

Details Some Explorations in Holomorphy Some Explorations in Holomorphy

1994-05-25

arxiv.org/abs/hep-th/9405155v2

Phys.Rev. D50 (1994) 5389-5397

Physics

High Energy Physics

High Energy Physics - Theory

(26 pages and 2 figures as one uuencoded PostScript file) SCIPP 94/11. Important references added; typos corrected

Scientific paper

10.1103/PhysRevD.50.5389

In supersymmetric theories, one can obtain striking results and insights by exploiting the fact that the superpotential and the gauge coupling function are holomorphic functions of the model parameters. The precise meaning of this holomorphy is subtle, and has been explained most clearly by Shifman and Vainshtein, who have stressed the role of the Wilsonian effective action. In this note, we elaborate on the Shifman-Vainshtein program, applying it to examples in grand unification, supersymmetric QCD and string theory. We stress that among the ``model parameters" are the cutoffs used to define the Wilsonian action itself, and that generically these must be defined in a field-dependent manner to obtain holomorphic results.

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