Renormalization group equations and the recurrence pole relations in pure quantum gravity

Abstract

In the framework of dimensional regularization, we propose a generalization of the renormalization group equations in the case of the perturbative quantum gravity that involves renormalization of the metric and of the higher order Riemann curvature couplings. The case of zero cosmological constant is considered. Solving the renormalization group (RG) equations we compute the respective beta functions and derive the recurrence relations, valid at any order in the Newton constant, that relate the higher pole terms $1/(d-4{)}^n$ to a single pole $1/(d-4)$ in the quantum effective action. Using the recurrence relations we find the exact form for the higher pole counter-terms that appear in 2, 3 and 4 loops and we make certain statements about the general structure of the higher pole counter-terms in any loop. We show that the complete set of the UV divergent terms can be consistently (at any order in the Newton constant) hidden in the bare gravitational action, that includes the terms of higher order in the Riemann tensor, provided the metric and the higher curvature couplings are renormalized according to the RG equations.

arXiv comment30 pages, 1 figure; equation numbering in sections 6 and 7 fixed

References in corpus (10)

• Is there a novel Einstein-Gauss-Bonnet theory in four dimensions?
• The renormalization group for non-renormalizable theories: Einstein gravity with a scalar field
• Hamiltonian formulation of f(Riemann) theories of gravity
• The basis of nonlocal curvature invariants in quantum gravity theory
• Some aspects of field equations in generalised theories of gravity
• Renormalization group equations for effective field theories
• Logarithmic terms in entropy of Schwarzschild black holes in higher loops
• RG Equations and High Energy Behaviour in Non-Renormalizable Theories
• Metric Redefinition and UV Divergences in Quantum Einstein Gravity
• Renormalization Group Treatment of Nonrenormalizable Interactions

Cited by in corpus (1)

• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity