BRST Symmetry Violation and Fundamental Limitations of Asymptotic Safety in Quantum Gravity

TL;DR

The paper argues that the asymptotic safety approach to quantum gravity is undermined by fundamental symmetry violations: canonical quantization shows general covariance fails above $\Lambda_{\text{grav}}$, and path-integral BRST gauge dependence confirms BRST symmetry breaking. Consequently, metric-based degrees of freedom cannot describe physics beyond $\Lambda_{\text{grav}}$, casting doubt on UV fixed points obtained in this regime. The work documents gauge-parameter dependence, non-convergent truncations up to high orders, experimental tensions, unitarity challenges, and obstructions to Wick rotation, all traced to the same root cause. It then advocates USMEG-EFT, an emergent-geometry EFT framework, which restricts to the consistent weak-field regime, yields definite graviton predictions (two tensor polarizations), and provides testable gravitational and SMEFT-corrected signals, thereby offering a physically viable path to quantum gravity. Overall, the paper promotes a paradigm shift from fundamental metric quantization to emergent spacetime with controlled effective field theory, aligning with robust experimental data like gravitational waves and preserving quantum consistency.

Abstract

The asymptotic safety program assumes that quantum gravity becomes renormalizable through ultraviolet fixed points in metric-based couplings. We demonstrate that this approach {encounters fundamental symmetry violations} across multiple independent criteria, all traceable to a single fundamental cause: the breakdown of general covariance and BRST symmetries above the gravitational cutoff scale. Rigorous canonical quantization proves that general covariance cannot be maintained quantum mechanically in dimensions greater than two, while recent path integral calculations reveal persistent gauge parameter dependence in quantum gravitational corrections, signaling BRST symmetry violation. These dual proofs establish that the metric tensor ceases to exist as a valid quantum degree of freedom above $Λ_{\text{grav}}$$\sim$$10^{18}$ GeV, rendering the search for ultraviolet fixed points in metric-based theories {problematic from a foundational physical perspective}. We provide comprehensive analysis demonstrating that asymptotic safety exhibits persistent gauge parameter dependence where fixed-point properties vary with arbitrary gauge choices, non-convergent truncation schemes extending to the 35th order showing no approach to stable values, experimental {tensions} with electroweak precision tests by orders of magnitude, matter content requirements incompatible with the Standard Model, absence of concrete graviton predictions due to gauge and truncation dependence, unitarity {challenges} through ghost instabilities and propagator negativity, and fundamental Wick rotation obstructions preventing reliable connection between Euclidean calculations and physical Lorentzian spacetime. We contrast this with the Unified Standard Model with Emergent Gravity framework that systematically avoids all asymptotic safety pathologies.