Scaling Solutions of Matter Form Factors in Asymptotically Safe Quantum Gravity
Alfio M. Bonanno, Diego Buccio, Emiliano M. Glaviano, Frank Saueressig
TLDR
This paper explores matter form factors in asymptotically safe quantum gravity, finding a non-trivial fixed point and scaling structure compatible with asymptotic safety.
Key contributions
- Investigates renormalization group flow of a scalar field minimally coupled to Einstein gravity.
- Derives and solves a flow equation for the scalar kinetic term's scale-dependent form factor.
- Discovers a non-trivial fixed point for the form factor, indicating non-canonical scaling behavior.
- Demonstrates this scaling structure is compatible with asymptotic safety in the non-local sector.
Why it matters
This work provides crucial insights into the behavior of matter fields within the framework of asymptotically safe quantum gravity. By identifying a non-trivial fixed point for matter form factors, it supports the viability of this approach for a consistent quantum theory of gravity.
Original Abstract
We investigate the renormalization group flow of a gravity--matter system in which a scalar field is minimally coupled to Einstein gravity and its kinetic term is given by a scale-dependent form factor $f_Λ(-\Box)$. Employing the Wilsonian proper-time flow equation, we derive a closed integro-differential equation that encodes the dependence of the form factor on the UV cutoff $Λ$. We solve the resulting fixed-point problem with a pseudospectral discretization and find a non-trivial fixed point for which $f_\ast(-\Box)$ departs from the canonical $-\Box$ behavior. Linearizing the flow about this solution yields a discrete spectrum of perturbations and a corresponding set of critical exponents, indicating a non-trivial scaling structure in this non-local sector compatible with asymptotic safety. We also observe that the form factor becomes local once the UV cutoff is removed, suggesting that the bare action associated with this fixed point is local in the scalar two-point sector.
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