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Article

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

by
Farrukh A. Chishtie
1,2
1
Peaceful Society, Science and Innovation Foundation, Vancouver, BC V6S 2K8, Canada
2
Department of Occupational Science and Occupational Therapy, University of British Columbia, Vancouver, BC V6T 2T4, Canada
Symmetry 2026, 18(1), 140; https://doi.org/10.3390/sym18010140 (registering DOI)
Submission received: 31 October 2025 / Revised: 5 January 2026 / Accepted: 6 January 2026 / Published: 10 January 2026
(This article belongs to the Special Issue Lorentz Invariance Violation and Space–Time Symmetry Breaking)

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 Λgrav1018 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.
Keywords: BRST symmetry; asymptotic safety; quantum gravity; gauge dependence; effective field theory; covariance breakdown; renormalization group; graviton phenomenology BRST symmetry; asymptotic safety; quantum gravity; gauge dependence; effective field theory; covariance breakdown; renormalization group; graviton phenomenology

Share and Cite

MDPI and ACS Style

Chishtie, F.A. BRST Symmetry Violation and Fundamental Limitations of Asymptotic Safety in Quantum Gravity. Symmetry 2026, 18, 140. https://doi.org/10.3390/sym18010140

AMA Style

Chishtie FA. BRST Symmetry Violation and Fundamental Limitations of Asymptotic Safety in Quantum Gravity. Symmetry. 2026; 18(1):140. https://doi.org/10.3390/sym18010140

Chicago/Turabian Style

Chishtie, Farrukh A. 2026. "BRST Symmetry Violation and Fundamental Limitations of Asymptotic Safety in Quantum Gravity" Symmetry 18, no. 1: 140. https://doi.org/10.3390/sym18010140

APA Style

Chishtie, F. A. (2026). BRST Symmetry Violation and Fundamental Limitations of Asymptotic Safety in Quantum Gravity. Symmetry, 18(1), 140. https://doi.org/10.3390/sym18010140

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