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February 8, 20260 citationsOpen Access

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

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FCFarrukh A. Chishtie

Key Points

  • This research explores the limitations of the asymptotic safety program in quantum gravity, focusing on symmetry violations.
  • Rigorous canonical quantization to analyze general covariance in higher dimensions.
  • Path integral calculations to assess gauge parameter dependence in quantum gravitational corrections.
  • Comparative analysis with the Unified Standard Model with Emergent Gravity framework.
  • General covariance cannot be maintained in quantum gravity above two dimensions.
  • Persistent BRST symmetry violations observed due to gauge dependence.
  • Asymptotic safety fails to produce stable fixed-point properties, encountering experimental inconsistencies.
  • Unified framework suggests spacetime geometry is emergent, avoiding issues faced by asymptotic safety.

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 Λgrav∼10¹⁸ 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. Each limitation independently challenges the program; collectively they establish fundamental incompatibility with quantum consistency requirements. We contrast this with the Unified Standard Model with Emergent Gravity framework, which recognizes general relativity as an effective field theory valid only below the covariance breakdown scale, systematically avoids all asymptotic safety pathologies, yields an emergent spin-2 graviton with transverse-traceless polarization confirmed by LIGO-Virgo observations, and provides definite experimental signatures across multiple domains. The fundamental limitations of asymptotic safety, established through theoretical analysis and experimental tension, demonstrates that consistent quantum gravity requires recognizing spacetime geometry as emergent rather than fundamental.

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Cite This Study

Farrukh A. Chishtie (2026) studied this question.

synapsesocial.com/papers/698827670fc35cd7a8846196https://doi.org/10.14288/1.0451425
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