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Quantum scale invariance on the lattice

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arxiv 0811.1967 v1 pith:OXNQOK2X submitted 2008-11-12 hep-th gr-qchep-lat

Mikhail E. Shaposhnikov , Igor I. Tkachev This is my paper
classification hep-thgr-qchep-lat
keywords latticefieldinvariancequantumscaletheoriesbrokenconstruction
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Weyl-invariant Einstein-Cartan gravity with a heavy ALP: Higgs Inflation and $\alpha$-attractors

    hep-ph 2025-07 conditional novelty 6.0 of 10

    In a Weyl-invariant Einstein-Cartan gravity theory with the SM Higgs and a heavy gravitational ALP, tuning two nonminimal couplings reproduces metric Higgs inflation and α-attractor-like inflation with ns≈1−2/N and r≈12/N^2.

  2. The Goldstone Awakens: Unimodular dark energy in scale-invariant $R^2$ gravity

    astro-ph.CO 2026-07 conditional novelty 5.0 of 10

    In a scale-invariant R² + unimodular-gravity model, the Goldstone boson of scale symmetry becomes thawing dark energy, with its equation of state fixed by the same coupling that sets the inflationary spectral tilt.

  3. Fermi scale from quantum gravity scaling solution

    hep-th 2026-01 conditional novelty 5.0 of 10

    The Fermi/Planck ratio is claimed to be predictable from the analyticity of the quantum-gravity scaling solution for the cosmon-Higgs coupling, with numerics showing the coupling flows to a tiny, near-critical value.

  4. Progress in Einstein-Cartan gravity

    hep-th 2025-06 conditional novelty 3.0 of 10

    A review of Weyl-invariant Einstein-Cartan gravity claiming that one extra axion-like scalar can unify the strong CP and hierarchy puzzles, with the hierarchy explained by tiny Lorentz gauge couplings.

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