An asymptotically safe solution to the U(1) triviality problem

Abstract

We explore whether quantum gravity effects within the asymptotic safety paradigm can provide a predictive ultraviolet completion for Abelian gauge theories. We evaluate the effect of quantum gravity fluctuations on the running couplings in the gauge sector and discover an asymptotically safe fixed point of the Renormalization Group. In particular, if the strength of gravitational interactions remains below a critical strength, the minimal gauge coupling becomes asymptotically free. Further, we point out that a completely asymptotically free dynamics for the gauge field is impossible to achieve, as asymptotically safe quantum gravity necessarily induces nonvanishing higher-order interactions for the gauge field in the ultraviolet.Comment: 6 pages plus references; 5 figures; version identical with published one; slight change in notation; discussion of effect of charged matter adde

Upper bound on the Abelian gauge coupling from asymptotic safety

“…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. Evidence for quantumgravity induced asymptotic freedom was already found in [33,34,37,39], where that same conclusion was reached for Abelian and non-Abelian gauge theories. Moreover, the interplay of quantum gravity and matter degrees of freedom results in an asymptotically safe fixed point at…”

“…Using that gauge and the perturbative approximation for the matter fields, such that all η A/φ from scalar-derivatives of the regulator are set to zero, we obtain The quantum-gravity contribution is exactly the one obtained in [34], if the additional coupling w 2 in that work is neglected. As in the TT approximation, an IR attractive fixed point at ρ * > 0 is induced if Λ < (4 + η h )/16.…”

“…Here, we extend these studies by exploring the possibility of an asymptotically safe, quantum-gravity induced UV completion for Abelian gauge theories, see also [33,34]. We restrict ourselves to the canonical interactions for scalar QED coupled to EinsteinHilbert gravity.…”

“…Physically, marginal irrelevance means a growth of the coupling towards the ultraviolet. Asymptotically safe quantum gravity adds a contribution to the beta function of all matter couplings that is linear in the matter coupling [1,16,[33][34][35][36][37][38][39][40][41][42][43][44][45][46]. If the sign of the gravitational contribution is negative, a fundamental change is triggered in the high-energy behavior of the corresponding coupling: the UV-repulsive free fixed point is turned into a UV attractive fixed point.…”

“…Alternatively, it can be extracted from the four-point function, where it provides the momentumindependent two-photon-scalar-antiscalar interaction. Finally, a rescaling of the gauge field A µ → 1 ρ A µ leads to a form of the action where the running coupling can be read off the gauge field propagator, as was done, e.g., in [34]. Gauge invariance of course implies that the running of ρ does not depend on how it is extracted.…”