2022/10/05 by Nobuyoshi Ohta, Ohta, Nobuyoshi
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2210.02583
openalex publication_date 2022/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a review of the one-loop divergences in higher derivative gravity theories. We first make the bilinear expansion in the quantum fluctuation on arbitrary backgrounds, introduce a higher-derivative gauge fixing and show that higher-derivative gauge fixing must have ghosts in addition to those naively expected. We give general formulae for the one-loop divergences in such theories, and give explicit results for theories with quadratic curvature terms. In this calculation, we need the heat kernel coefficients for the four-derivative minimal operators and two-derivative nonminimal vector operators, which are summarized. We also discuss the beta functions in the renormalization group, and show that the dimensionless couplings are asymptotically free. The calculation is also extended to the theories with arbitrary functions of R and Rμν2. We show that the result is independent of metric parametrization and gauge on shell.