Márk Tarnai, Balázs Szigeti, Gergely Gábor Barnaföldi (2026.10.01 - 12.31)

Abstract: Unifying relativistic field theories and gravity on microscopic scales remains an unresolved problem to this day. Within the scope of our research, we examined the problem of quantum corrections in a simplified model: spherically symmetric, asymptotically safe quantum gravity. Self-similarity manifests as a geometric homothetic symmetry in general relativity describing gravitation. In the quantum gravity limit, there is likewise a scaling self-similar behaviour determined by the functional renormalisation group (FRG) equations of the effective action. The question arises whether these two symmetries might be connected. If so, it could pave the way toward a deeper understanding of the mathematical structure of asymptotically convergent quantum gravity. In our research, we investigated under what conditions quantum corrections preserve or modify the initial homothetic symmetry in a spherically symmetric dilaton gravity model. Based on the general Wetterich equations corresponding to this model, we determined the scale dependence of the couplings to clarify the geometric meaning of fixed-point scale invariance.