Is scale-invariance in gauge-Yukawa systems compatible with the graviton?

Abstract

We explore whether perturbative interacting fixed points in matter systems can persist under the impact of quantum gravity. We first focus on semi-simple gauge theories and show that the leading order gravity contribution evaluated within the functional Renormalization Group framework preserves the perturbative fixedpoint structure in these models discovered in [1]. We highlight that the quantumgravity contribution alters the scaling dimension of the gauge coupling, such that the system exhibits an effective dimensional reduction. We secondly explore the effect of metric fluctuations on asymptotically safe gauge-Yukawa systems which feature an asymptotically safe fixed point [2]. The same effective dimensional reduction that takes effect in pure gauge theories also impacts gauge-Yukawa systems. There, it appears to lead to a split of the degenerate free fixed point into an interacting infrared attractive fixed point and a partially ultraviolet attractive free fixed point. The quantum-gravity induced infrared fixed point moves towards the asymptotically safe fixed point of the matter system, and annihilates it at a critical value of the gravity coupling. Even after that fixed-point annihilation, graviton effects leave behind new partially interacting fixed points for the matter sector.

Asymptotic safety of gravity with matter

“…VII B 1, VII B 2, and VII B 3 if the gaugematter system is itself ultraviolet stable. For example, one flavor QED exhibits a UV-Landau pole and is stabilized by gravity, which makes the combined system asymptotically safe, for a comprehensive analysis see [85,88]. Adding more flavors potentially destabilizes the system; however, such an analysis has to avoid the interpretation of the seeming failure of asymptotic safety described here.…”

Effective action for the Yukawa model in curved spacetime

“…This has been done within the asymptotic safety program [25][26][27][28][29] and also using more standard perturbative methods [30][31][32][33][34]. (See also the illuminating discussion of [35].…”

Phase structure of completely asymptotically free SU( Nc ) models with quarks and scalar quarks

“…The existence of controllable nonsupersymmetric models with interacting UV fixed points led to the recent discovery [20] that the addition of positive mass-squared terms leads to calculable radiative symmetry breaking in the IR, a phenomenon akin to the radiative symmetry breaking that occurs in the supersymmetric standard model [21]. We will not consider gravitational corrections which, however, are the subject of interesting related work [22][23][24].…”