Low energy quantum gravity from the effective average action

Within the effective average action approach to quantum gravity, we recover the low-energy effective action as derived in the effective field theory framework by studying the flow of possibly nonlocal form factors that appear in the curvature expansion of the effective average action. We restrict to the one-loop flow where progress can be made with the aid of the nonlocal heat kernel expansion. We discuss the possible physical implications of the scale-dependent low-energy effective action through the analysis of the quantum corrections to the Newtonian potential.

Figure 1

The functions $g_1(u)-\frac{1}{60}$ (upper curve) and $g_2(u)-\frac{7}{10}$ (lower curve), representing the flow of the form factors in (17) after we imposed the UV boundary conditions (25), as a function of $u$. Note that the flow stops for $x<4k^2$: only IR or slow modes contribute effectively to the RG running of the form factors.