Asymptotically Safe Lorentzian Gravity

The gravitational asymptotic safety program strives for a consistent and predictive quantum theory of gravity based on a nontrivial ultraviolet fixed point of the renormalization group (RG) flow. We investigate this scenario by employing a novel functional renormalization group equation which takes the causal structure of space-time into account and connects the RG flows for Euclidean and Lorentzian signature by a Wick rotation. Within the Einstein-Hilbert approximation, the $\beta$ functions of both signatures exhibit ultraviolet fixed points in agreement with asymptotic safety. Surprisingly, the two fixed points have strikingly similar characteristics, suggesting that Euclidean and Lorentzian quantum gravity belong to the same universality class at high energies.

Figure 1

Phase portraits obtained from the numerical integration of the Euclidean (top) and Lorentzian (bottom) $\beta$ functions with $m=2\pi$. The Euclidean flow diagram completely agrees with the covariant result [24].