Quantum scale invariance on the lattice

Understand

We propose a scheme leading to a non-perturbative definition of lattice field theories which are scale-invariant on the quantum level.

• A key idea of the construction is the replacement of the lattice spacing by a propagating dynamical field -- the dilaton.
• We describe how to select non-perturbatively the phenomenologically viable theories where the scale invariance is broken spontaneously.
• Relation to gravity is also discussed.