Asymptotic safety of gravity with matter

Abstract

We study the asymptotic safety conjecture for quantum gravity in the presence of matter fields. A general line of reasoning is put forward explaining why gravitons dominate the high-energy behavior, largely independently of the matter fields as long as these remain sufficiently weakly coupled. Our considerations are put to work for gravity coupled to Yang-Mills theories with the help of the functional renormalization group. In an expansion about flat backgrounds, explicit results for beta functions, fixed points, universal exponents, and scaling solutions are given in systematic approximations exploiting running propagators, vertices, and background couplings. Invariably, we find that the gauge coupling becomes asymptotically free while the gravitational sector becomes asymptotically safe. The dependence on matter field multiplicities is weak. We also explain how the scheme dependence, which is more pronounced, can be handled without changing the physics. Our findings offer a new interpretation of many earlier results, which is explained in detail. The results generalize to theories with minimally coupled scalar and fermionic matter. Some implications for the ultraviolet closure of the Standard Model or its extensions are given.

Form factors in asymptotic safety: conceptual ideas and computational toolbox

“…This indicates that our analysis provides the first study of the gravity-matter fixed point identified in [12,31,83,100] at the level of self-consistent form factors. Comparing the critical exponents (112) and (113) furthermore suggests that the properties of the fixed point are essentially determined by the gravitational contributions [100]. Including a self-consistent form factor in the scalar sector has a very mild effect on the stability coefficients.…”

Dark matter meets quantum gravity

“…Typical values of f g are of the order O(10 −2 ) [41] and here we use f g ≤ 0.04. Gravity supports asymptotic freedom for non-abelian gauge theories and the gauge couplings run in the Gaußian fixed point g * = 0 [64,66]. This Gaußian fixed point is relevant and thus the gauge couplings approach it slowly beyond the Planck scale.…”

“…Again,G = Gµ 2 andΛ = Λ/µ 2 are the dimensionless versions of the Newton coupling and cosmological constant. Importantly, f g is positive for all relevant values of the gravity couplings, see [66], which makes the contribution to the beta function negative. Typical values of f g are of the order O(10 −2 ) [41] and here we use f g ≤ 0.04.…”

“…We now discuss the graviton contribution to the running of the gauge coupling, which were computed, e.g., in [42,[62][63][64][65][66]. We again split the beta function in the standard matter part β g,matter and into a gravity part f g g:…”

Grand unified theories in renormalisable, classically scale invariant gravity

“…For some recent work on AS, see Refs [13][14][15],. and for references to work up to 2017, see Ref [16].…”