A Scaleful Theory
Abstract: Relativistic quantum field theories become scale-free (conformal) at short distances. On the other hand, gravitational theories are expected to keep memory of the Planck scale at arbitrarily high energies. I will describe a class of exactly solvable relativistic models which exhibit a new type of asymptotic behavior and never loose memory of the fundamental scale. In spite of their simplicity, these models exhibit surprisingly many properties expected from a more mature gravitational theories. In particular, they do not allow for sharply defined local observables.
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