Gravitational Fixed Points from Perturbation Theory

The fixed point structure of the renormalization flow in higher derivative gravity is investigated in terms of the background covariant effective action using an operator cutoff that keeps track of powerlike divergences. Spectral positivity of the gauge fixed Hessian can be satisfied upon expansion in the asymptotically free higher derivative coupling. At one-loop order in this coupling strictly positive fixed points are found for the dimensionless Newton constant $g_N$ and the cosmological constant $\lambda$, which are determined solely by the coefficients of the powerlike divergences. The renormalization flow is asymptotically safe with respect to this fixed point and settles on a $\lambda (g_N)$ trajectory after $O(10)$ units of the renormalization mass scale to accuracy ${10}^{-7}$.

Figure 1

Wilsonian one-loop flow (5, 6, 17).