One-loop effective action for quantum gravity plus matter is computed off-shell in a general background gauge, shown to be gauge-independent on-shell per the DeWitt-Kallosh theorem, and used to establish non-renormalizability.
Renormalization of gauge theories in the background-field approach
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abstract
Using the background-field method we demonstrate the Becchi-Rouet-Stora-Tyutin (BRST) structure of counterterms in a broad class of gauge theories. Put simply, we show that gauge invariance is preserved by renormalization in local gauge field theories whenever they admit a sensible background-field formulation and anomaly-free path integral measure. This class encompasses Yang-Mills theories (with possibly Abelian subgroups) and relativistic gravity, including both renormalizable and non-renormalizable (effective) theories. Our results also hold for non-relativistic models such as Yang-Mills theories with anisotropic scaling or Horava gravity. They strengthen and generalize the existing results in the literature concerning the renormalization of gauge systems. Locality of the BRST construction is emphasized throughout the derivation. We illustrate our general approach with several explicit examples.
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UNVERDICTED 3representative citing papers
Develops a Lagrangian path integral formulation for non-projectable Hořava gravity and computes one-loop divergences in (2+1) dimensions, verifying cancellation of linear-in-frequency terms to extract beta functions for Newton constant and λ.
Dyson-Schwinger methods applied to gravity theories produce conformally flat metrics and a sequence of cosmological phase transitions from conformal symmetry breaking that non-minimal scalar couplings can suppress.
citing papers explorer
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Quantum gravity and matter fields in a general background gauge
One-loop effective action for quantum gravity plus matter is computed off-shell in a general background gauge, shown to be gauge-independent on-shell per the DeWitt-Kallosh theorem, and used to establish non-renormalizability.
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Quantizing non-projectable Ho\v{r}ava gravity with Lagrangian path integral
Develops a Lagrangian path integral formulation for non-projectable Hořava gravity and computes one-loop divergences in (2+1) dimensions, verifying cancellation of linear-in-frequency terms to extract beta functions for Newton constant and λ.
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Review of strongly coupled regimes in gravity with Dyson-Schwinger approach
Dyson-Schwinger methods applied to gravity theories produce conformally flat metrics and a sequence of cosmological phase transitions from conformal symmetry breaking that non-minimal scalar couplings can suppress.