I would like to know (1) what exactly is a UV-complete theory and (2) what is a confirmatory test of that?
Is asymptotic freedom enough to conclude that a theory is UV-complete?
Does it become conclusive a test if the beta-function is shown to be non-perturbatively negative?
If the one-loop beta-function is negative then does supersymmetry (holomorphy) immediately imply that the beta-function is non-perturbatively negative and hence the theory is proven to be UV-complete?
Or is vanishing of the beta-function enough to conclude that theory is UV-complete?
Again similarly does supersymmetry (holomorphy) guarantee that if the 1-loop beta function is vanishing then it is non-perturbatively so and hence the theory is UV-complete?
Does superconformal theory necessarily mean UV-complete? We know that there exists pairs of superconformal theories with different gauge groups - related by S-duality - which have the same partition function - what does this say about UV-completeness?
Does a theory being UV-complete necessarily mean that it has a Maldacena dual? (...and isn't that the meaning of AdS/CFT that every UV-complete theory has a string dual and vice-versa?..)