Asymptotic Safety in Higher-Derivative Gravity

Abstract

We study the non-perturbative renormalization group flow of higher-derivative gravity employing functional renormalization group techniques. The non-perturbative contributions to the β-functions shift the known perturbative ultraviolet fixed point into a non-trivial fixed point with three UV-attractive and one UV-repulsive eigendirections, consistent with the asymptotic safety conjecture of gravity. The implication of this transition on the unitarity problem, typically haunting higher-derivative gravity theories, is discussed.Among the many approaches to quantum gravity, a special place is occupied by higherderivative gravity, which, besides the Einstein-Hilbert term, also includes fourth-order operators in the action. Indeed, the higher-derivative propagators soften the divergences encountered in the perturbative quantization, rendering the theory perturbatively renormalizable [1] and asymptotically free at the one-loop level [2,3,4,5,6]. Unfortunately, the extra terms responsible for the improved UV behavior also induce massive negative norm states [7], so-called "poltergeists", which led to the belief that the theory is not unitary. Several arguments suggest that this shortcoming can be cured by quantum effects [2,8], but the lack of non-perturbative methods has made it hard to substantiate such claims.Recently, the question of renormalizability has received renewed attention due to mounting evidence in favor of the non-perturbative renormalizability, or asymptotic safety (AS), of gravity [9,10,11,12]. In this scenario, the ultraviolet (UV) behavior of the theory is controlled by a

Gauges and functional measures in quantum gravity II: higher-derivative gravity

“…These are all the divergences that arise at one loop in d = 4. The method we have used is a one-loop approximation of the single-field approximation of the exact RG equation for gravity, as first derived in [31] for the EH-case and then extended to HDG in [24,[34][35][36], to 3d topologically massive gravity in [40], and beyond the one-loop approximation in [41][42][43][44].…”

Matter matters in asymptotically safe quantum gravity

“…The resulting expressions are considerably more complicated than the ones appearing in eq. (23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34). In particular they are rational functions inΛ andG whose numerators and denominators are polynomials of higher order than the ones appearing in the leading one loop terms.…”

“…Evidence for the existence of a gravitational fixed point with a finite number of relevant directions has been collected with a variety of tools, but in recent years most progress has come from functional Renormalization Group methods, whose application to gravity has been pioneered in [18]. Various nonperturbative truncations of the RG flow indicate the existence of an interacting fixed point [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. Recent results also suggest the existence of an infrared fixed point [35][36][37].…”

Probing the quantum nature of spacetime by diffusion

“…2 Expressing this metric through a fixed reference scale leads to a modified diffusion equation providing an effective description of the propagation of the probe particle on the quantum gravity background. For asymptotically safe gravity [19][20][21][22] in d dimensions, this procedure gives rise to a multifractal structure where the spectral dimension is of the form [9] d S = 2d 2 + δ .…”