Asymptotic solutions in asymptotic safety
arXiv:1704.08873 · doi:10.1103/PhysRevD.95.106010
Abstract
We explain how to find the asymptotic form of fixed point solutions in functional truncations, in particular approximations. We find that quantum fluctuations do not decouple at large , typically leading to elaborate asymptotic solutions containing several free parameters. By a counting argument, these can be used to map out the dimension of the fixed point solution spaces. They are also necessary to validate the numerical solution, and provide the physical part in the limit that the cutoff is removed: the fixed point equation of state. As an example we apply the techniques to a recent approximation by Demmel et al, finding asymptotic matches to their numerical solution. Depending on the value of the endomorphism parameter, we find many other asymptotic solutions and fixed point solution spaces of differing dimensions, yielding several alternative scenarios for the equation of state. Asymptotic studies of other approximations are needed to clarify the picture.
Minor corrections. Version to be published in PRD
References in corpus (14)
- Exact evolution equation for the effective potential
- On the renormalization group flow of f(R)-gravity
- Asymptotic safety in the f(R) approximation
- Search of scaling solutions in scalar-tensor gravity
- The Renormalization Group flow of unimodular f(R) gravity
- The local potential approximation in quantum gravity
- Quantum gravity and Standard-Model-like fermions
- Renormalization Group Equation for gravity on hyperbolic spaces
- Fixed-Functionals of three-dimensional Quantum Einstein Gravity
- Large curvature and background scale independence in single-metric approximations to asymptotic safety
- Background independent exact renormalization group for conformally reduced gravity
- The background scale Ward identity in quantum gravity
- Four-Derivative Quantum Gravity Beyond Perturbation Theory
- Fixed Functionals in Asymptotically Safe Gravity