Gravitational fixed points and asymptotic safety from perturbation theory
201045 pages
Published in:
- Nucl.Phys.B 833 (2010) 226-270
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Abstract: (Elsevier)
The fixed point structure of the renormalization flow in Einstein gravity and higher derivative gravity is investigated in terms of the background effective action. A refined perturbative framework is developed consisting of: use of a covariant op erator regularization that keeps track of powerlike divergences, a non-minimal subtraction ansatz for the originally dimensionful couplings in combination with a 'Wilsonian' matching condition, and the construction of a one-loop effective action exactly g auge-independent on-shell in regularized form. Using this framework strictly positive fixed points for the dimensionless Newton constant g_N and the cosmological constant @l can be identified already in one-loop perturbation theory. The renormalization fl ow is asymptotically safe with respect to the nontrivial fixed points in both cases. In Einstein gravity a residual gauge dependence of the fixed points is unavoidable while in higher derivative gravity both the fixed point and the flow equations are univ ersal. Along this flow spectral positivity of the Hessians can be satisfied, thereby meeting an essential condition for a well-defined Euclidean field theory setting. Dependence on O(10) initial data is erased to accuracy 0.5% after O(100) units of the re normalization mass scale and the flow settles on a @l(g_N) orbit.- derivative: high
- gravitation: fundamental constant
- renormalization
- operator: regularization
- fixed point
- flow
- perturbation theory
- asymptotic safety
- gravitation: model
- general relativity
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