Abstract
Using the nonrenormalization theorem and Pohlmeyer's theorem, it is proven that there cannot be an asymptotic safety scenario for the Wess–Zumino model unless there exists a non-trivial fixed point with (i) a negative anomalous dimension (ii) a relevant direction belonging to the Kähler potential.
Highlights
Using the nonrenormalization theorem and Pohlmeyer’s theorem, it is proven that there cannot be an asymptotic safety scenario for the Wess-Zumino model unless there exists a non-trivial fixed point with (i) a negative anomalous dimension (ii) a relevant direction belonging to the Kahler potential
It will be proven that, for such an asymptotic safety scenario [2] to occur, the putative fixed point must have both a negative anomalous dimension1 and at least one relevant operator belonging to the Kahler potential
To formulate our argument, we introduce the Wilsonian effective action, SΛ, constructed by integrating out degrees of freedom between the bare scale and a lower, effective scale, Λ.2
Summary
Using the nonrenormalization theorem and Pohlmeyer’s theorem, it is proven that there cannot be an asymptotic safety scenario for the Wess-Zumino model unless there exists a non-trivial fixed point with (i) a negative anomalous dimension (ii) a relevant direction belonging to the Kahler potential. We will consider the existence of certain renormalization group fixed points in theories of a chiral superfield. Suppose that a non-trivial fixed point exists and, that there is a renormalized trajectory [1] emanating from it, such that the low energy effective theory is well described by the Wess-Zumino model.
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