Dimensionless physics

Abstract

We discuss two scenarios of emergent gravity. In one of them the quantum vacuum is considered as superplastic crystal, and the effective gravity describes the dynamical elastic deformations of this crystal. In the other one the gravitational tetrads emerge as the bilinear form of the fermionic fields. In spite of the essentially different mechanisms of emergent gravity, these two scenarios have one important common property: the metric field has dimension of the inverse square of length $[g_{\mu \nu }]=1/[l{]}^2$, as distinct from the conventional dimensionless metric, $[g_{\mu \nu }]=1$, in general relativity. As a result the physical quantities, which obey diffeomorphism invariance, become dimensionless. This takes place for such quantities as Newton constant, the scalar curvature, the cosmological constant, particle masses, fermionic and scalar bosonic fields, etc. This may suggest that the dimensionless physics can be the natural consequence of the diffeomorphism invariance, and thus can be the general property of any gravity, which emerges in the quantum vacuum. One of the nontrivial consequences of the shift of dimensions is related to topology. Due to the shift of dimensions some operators become topological, and contain the integer or fractional prefactors in the action. This in particular concerns the intrinsic 3+1 quantum Hall effect and the Nieh-Yan quantum anomaly in terms of torsion.

8 pages, no figures, extended version of arXiv:2003.00915, draft prepared for the issue of JETP devoted to Dzyaloshinskii-90

References in corpus (8)

• Dynamic vacuum variable and equilibrium approach in cosmology
• Gluonic vacuum, q-theory, and the cosmological constant
• Torsion, Parity-odd Response and Anomalies in Topological States
• Area spectrum of the D-dimensional de Sitter spacetime
• How fundamental are fundamental constants?
• Elie Cartan's torsion in geometry and in field theory, an essay
• Theory of the fractional quantum Hall effect in Weyl semimetals
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Cited by in corpus (9)

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• Clifford algebra Cl(0,6) approach to beyond the standard model and naturalness problems
• On Torsion Contribution to Chiral Anomaly via Nieh-Yan Term
• Acoustic metric and Planck constants
• Dimensionless physics: Planck constant as an element of Minkowski metric