Abstract
We analyze the $\mathcal{N}=1$ supersymmetric Wess-Zumino model dimensionally reduced to the $\mathcal{N}=2$ supersymmetric model in three Euclidean dimensions. As in the original model in four dimensions and the $\mathcal{N}=(2,2)$ model in two dimensions the superpotential is not renormalized. This property puts severe constraints on the non-trivial fixed-point solutions, which are studied in detail. We admit a field-dependent wave function renormalization that in a geometric language relates to a K\"ahler metric. The K\"ahler metric is not protected by supersymmetry and we calculate its explicit form at the fixed point. In addition we determine the exact quantum dimension of the chiral superfield and several critical exponents of interest, including the correction-to-scaling exponent $\omega$, within the functional renormalization group approach. We compare the results obtained at different levels of truncation, exploring also a momentum-dependent wave function renormalization. Finally we briefly describe a tower of multicritical models in continuous dimensions.
Highlights
In the challenge of understanding strongly interacting quantum field theories, progress has often been associated with the special role played by symmetries
Both in the three-dimensional as well as in the lowerdimensional multicritical case, we especially focus on the determination of the first correction-to-scaling exponent ω, which is the less irrelevant critical exponent not constrained by supersymmetry
We believe that this work crucially contributes to improve the state-ofthe-art picture of critical WZ models. These results are obtained by means of the functional renormalization group (FRG), a general method that can be applied to any strongly interacting quantum field theory in a continuous number of dimensions, whose adaptation to the present WZ models is discussed in Sec
Summary
In the challenge of understanding strongly interacting quantum field theories, progress has often been associated with the special role played by symmetries. We believe that this work crucially contributes to improve the state-ofthe-art picture of critical WZ models These results are obtained by means of the functional renormalization group (FRG), a general method that can be applied to any strongly interacting quantum field theory in a continuous number of dimensions, whose adaptation to the present WZ models is discussed in Sec. III within the threedimensional parametrization. Other studies with different tools would be helpful to get a more comprehensive picture of scaleinvariant WZ models with four supercharges This is the goal of the present work, which provides constructive evidence in favor of the field theoretic consistency of these models, within the FRG framework for the first time.
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