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

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 $\Lambda_{\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.