Quantum Distortion Gravity: Classical Foundations, Gauge Structure and the Einstein–Hilbert Flow with QDG-Like Matter

Abstract

Quantum Distortion Gravity (QDG) is a metric-affine proposal in which the affine connection is an independent field and Weyl invariance is gauged with a dilaton compensator. This paper collects what can be stated and checked about it. Classically: the irreducible decomposition 64=4+12+48 of the distortion tensor and its quadratic invariants (with the convention for the cyclic invariant stated explicitly and the effect of the transposed one listed); a no-go statement showing that no bare quadratic invariant of the distortion is Weyl invariant, because of its homogeneous weight, with the full local variation and the family that is invariant under the inhomogeneous shift alone; the Weyl-invariant truncated action with free coefficients and its reduction in unitary gauge to Einstein gravity plus two massive vector fields. Constraint and gauge structure: eight propagating bosonic degrees of freedom at quadratic order (a linearised count, tree-level unitarity only, with a C² term generated at one loop, so no ghost-freedom claim); BRST nilpotency and the classical master equation of WeylrtimesDiff; the status of the Weyl anomaly, whose coefficients for the gauged symmetry are not known. Quantum flow: the Einstein&ndash;Hilbert flow from the Wetterich equation (optimised cutoff, harmonic gauge, linear split, S⁴) with minimally coupled matter of QDG-like content (n_f Dirac fermions and two Proca fields in the massless limit) reduces to a cubic equation. A non-Gaussian fixed point exists for every n_f<10; at n_f=3 it is at (G̃_*,λ_*)=(2.73,-0.318) with real exponents (2.21,0.72), exists for nine of nine regulators, but moves strongly with the regulator and with the matter-cutoff convention. A phenomenological flow used in earlier versions is kept, labelled as a model. The Weyl-gauged sector of QDG is not part of the flow, so the paper establishes no statement of asymptotic safety for QDG itself.

Parole chiave

• Quantum Distortion Gravity
• Asymptotic Safety
• Renormalization Group
• Black Hole Entropy
• Ghost-Free Unitarity
• Metric-Affine Gravity
• Torsion
• Non-Metricity

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