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On limit cycles in supersymmetric theories. (English) Zbl 1370.81160

Summary: Contrary to popular belief conformality does not require zero beta functions. This follows from the work of Jack and Osborn, and examples in non-supersymmetric theories were recently found by some of us. In this letter, we show that such examples are absent in unitary \(\mathcal{N} = 1\) supersymmetric four-dimensional field theories. More specifically, we show to all orders in perturbation theory that the beta-function vector field of such theories does not admit limit cycles. A corollary of our result is that unitary \(\mathcal{N} = 1\) supersymmetric four-dimensional theories cannot be superscale-invariant without being superconformal.

MSC:

81T60 Supersymmetric field theories in quantum mechanics
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