Does minimum length prevent conformal symmetry?

Question

Or conversely, is there a way to combine conformal symmetry and minimum length (such as the Planck length)?

Are there papers exploring this possibility?

Comments

Where does this idea of a minimum length come from?

Normally, in any physical problem, say in QM, there are characteristic lengths like the Bohr radius $a_0$ and alike, but the space coordinates run from zero to infinity, so there are shorter lengths than $a_0$. Similarly with the Plank length - there are shorter distances than it. At high enough energies $E$ you will reach much shorter distances. You may consider it as a "conformal symmetry" limit, if you like.

If you decide just to impose the smallest length with no physical justification, it is not physics anymore. Do discrete space modelling instead and call it a "discrete modelling" whatever the minimal length you chose. Even then you may have high enough energies $E$ that correspond to shorter distances, I guess. Or you want to impose the "maximal energy" $E_{\text{max}}$ in your theory?

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