Asymptotic safety of gravity-matter systems

Abstract

We study the ultraviolet stability of gravity-matter systems for general numbers of minimally coupled scalars and fermions. This is done within the functional renormalisation group setup put forward in \cite{Christiansen:2015rva} for pure gravity. It includes full dynamical propagators and a genuine dynamical Newton's coupling, which is extracted from the graviton three-point function. We find ultraviolet stability of general gravity-fermion systems. Gravity-scalar systems are also found to be ultraviolet stable within validity bounds for the chosen generic class of regulators, based on the size of the anomalous dimension. Remarkably, the ultraviolet fixed points for the dynamical couplings are found to be significantly different from those of their associated background counterparts, once matter fields are included. In summary, the asymptotic safety scenario does not put constraints on the matter content of the theory within the validity bounds for the chosen generic class of regulators.Comment: 19 pages, 10 figure

Upper bound on the Abelian gauge coupling from asymptotic safety

“…For positive G, Λ < 1/2 (and η h < 16(1 − Λ) as is also required for our choice of regulator, see [17]), the quantum-gravity contribution renders the gauge coupling asympotically free. For positive η h , the critical value of Λ, for which quantum gravity counteracts asymptotic freedom, is shifted further away from the boundary at Λ = 1/2.…”

“…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…”

On avoiding Ostrogradski instabilities within Asymptotic Safety

“…While all studies agree on the statement that the matter content of the standard model of particle physics leads to a fixed point structure suitable for realizing the Asymptotic Safety mechanism, the precise values for N s , N v , and N D supporting a NGFP are different. Restricting to the cases where the matter sector contains scalar fields only, [17][18][19][20] report an upper bound N s 16 − 20, while in [21] no such bound is present in agreement with the initial works [22,23]. This difference can be traced back to different choices for the coarse graining operators and definitions of Newton's constant employed in these works.…”

“…[17][18][19][20] studied projections of the full RG flow where the matter sector contained an arbitrary number of minimally coupled scalars N s , vectors N v , and Dirac fermions N D . Complementary results for the case where spacetime carries a foliation structure have been reported in [21].…”

“…[18][19][20] define Newton's constant based on the flat space graviton propagator while [17,21] resort to a background Newton's constant. As argued in [19] matter degrees of freedom contribute differently in these settings. The two pictures are in qualitative agreement if N s is small but start to deviate once the matter contribution becomes significant.…”