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Functional Renormalisation for $f(R_{\mu\nu\rho\sigma})$ Quantum Gravity

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arxiv 2202.10436 v2 pith:WEQ5VSBL submitted 2022-02-21 hep-th gr-qc

classification hep-thgr-qc
keywords gravityquantumcurvatureextensionsflowsfunctionalgeneraloperator
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We derive new functional renormalisation group flows for quantum gravity, in any dimension. The key new achievement is that the equations apply for any theory of gravity whose underlying Lagrangian $\sim f(R_{\mu\nu\rho\sigma})$ is a function of the Riemann tensor and the inverse metric. The results centrally exploit the benefits of maximally symmetric spaces for the evaluation of operator traces. The framework is highly versatile and offers a wide range of new applications to study quantum gravitational effects in extensions of Einstein gravity, many of which have hitherto been out of reach. The phase diagram and sample flows for Einstein-Hilbert gravity, Gauss-Bonnet, and selected higher-order theories of gravity are given. We also provide an algorithm to find the flow for general polynomial Riemann curvature interactions. The setup vastly enhances the reach of fixed point searches, enabling novel types of search strategies including across the operator space spanned by polynomial curvature invariants, and in extensions of general relativity relevant for cosmology. Further implications, and links with unimodular versions of gravity are indicated.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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