The r0 symmetry is preserved at one-loop in the r0-invariant two-Higgs Doublet Model if the UV cutoff squared transforms non-trivially under r0; the minimal model requires two real fields.
Jackiw, Functional evaluation of the effective poten- tial, Phys
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Imaginary scaling invariance of the one-loop effective potential
The r0 symmetry is preserved at one-loop in the r0-invariant two-Higgs Doublet Model if the UV cutoff squared transforms non-trivially under r0; the minimal model requires two real fields.