Gravitational Two-Loop Counterterm Is Asymptotically Safe

Abstract

Weinberg's asymptotic safety scenario provides an elegant mechanism to construct a quantum theory of gravity within the framework of quantum field theory based on a non-Gaußian fixed point of the renormalization group flow. In this work we report novel evidence for the validity of this scenario, using functional renormalization group techniques to determine the renormalization group flow of the Einstein-Hilbert action supplemented by the two-loop counterterm found by Goroff and Sagnotti. The resulting system of beta functions comprises three scale-dependent coupling constants and exhibits a non-Gaußian fixed point which constitutes the natural extension of the one found at the level of the Einstein-Hilbert action. The fixed point exhibits two ultraviolet attractive and one repulsive direction supporting a low-dimensional UV-critical hypersurface. Our result vanquishes the longstanding criticism that asymptotic safety will not survive once a "proper perturbative counterterm" is included in the projection space.

Upper bound on the Abelian gauge coupling from asymptotic safety

“…We focus on an asymptotically safe model of quantum gravity [4]. Based on the groundbreaking work of Reuter [5], compelling evidence for the existence of an asymptotically safe fixed point in pure gravity [6][7][8][9][10][11][12][13][14] as well as with matter [15][16][17][18][19] has been discovered, for reviews see, e.g., [20][21][22][23][24][25][26][27][28][29][30][31][32]. This fixed point provides a UV completion for a quantum field theory of the…”

Composite operators in asymptotic safety

“…For example, employing the optimized cutoff [37] one finds explicitly: 8) with the function F defined by…”

Quantum gravity on foliated spacetimes: Asymptotically safe and sound

“…Over the years a series of complementary approaches capable of testing the Asymptotic Safety hypothesis have been developed. Starting from the pioneering work [14], functional renormalization group methods have established the existence of a suitable NGFP in a wide range of approximations , including the demonstration that the NGFP persists in the presence of the perturbative two-loop counterterm [48] and upon including an infinite number of scale-dependent couplings [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63]. Moreover, a first step connecting the NGFP to the underlying conformal field theory appeared in [64], possible completions of the flow at low energy have been discussed in [17,24,38,40,41] and geometric arguments determining the scaling of Newton's constant at the NGFP have been forwarded in [65,66].…”