Wilsonian Proof for Renormalizability of N=1/2 Supersymmetric Field Theories

Abstract

We provide Wilsonian proof for renormalizability of four-dimensional quantum field theories with $\mathcal{N}=1/2$ supersymmetry. We argue that the non-hermiticity inherent to these theories permits assigning noncanonical scaling dimension both for the Grassman coordinates and superfields. This reassignment can be done in such a way that the non(anti)commutativity parameter is dimensionless, and then the rest of the proof ammounts to power counting. The renormalizability is also stable against adding standard four-dimensional soft-breaking terms to the theory. However, with the new scaling dimension assignments, some of these terms are not just relevant deformations of the theory but become marginal.

10 pages, no figure, v2: minor correction

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• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
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