Fixed-Functionals of three-dimensional Quantum Einstein Gravity
arXiv:1208.2038 · doi:10.1007/JHEP11(2012)131
Abstract
We study the non-perturbative renormalization group flow of f(R)-gravity in three-dimensional Asymptotically Safe Quantum Einstein Gravity. Within the conformally reduced approximation, we derive an exact partial differential equation governing the RG-scale dependence of the function f(R). This equation is shown to possess two isolated and one continuous one-parameter family of scale-independent, regular solutions which constitute the natural generalization of RG fixed points to the realm of infinite-dimensional theory spaces. All solutions are bounded from below and give rise to positive definite kinetic terms. Moreover, they admit either one or two UV-relevant deformations, indicating that the corresponding UV-critical hypersurfaces remain finite dimensional despite the inclusion of an infinite number of coupling constants. The impact of our findings on the gravitational Asymptotic Safety program and its connection to new massive gravity is briefly discussed.
34 pages, 14 figures
References in corpus (21)
- Massive Gravity in Three Dimensions
- More on Massive 3D Gravity
- Asymptotic safety in higher-derivative gravity
- Ultraviolet properties of f(R)-Gravity
- On the renormalization group flow of f(R)-gravity
- Taming perturbative divergences in asymptotically safe gravity
- Bimetric Renormalization Group Flows in Quantum Einstein Gravity
- Ghost anomalous dimension in asymptotically safe quantum gravity
- Ising exponents from the functional renormalisation group
- Matter Induced Bimetric Actions for Gravity
- Background Independence and Asymptotic Safety in Conformally Reduced Gravity
- The Universal RG Machine
- Conformal sector of Quantum Einstein Gravity in the local potential approximation: non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance
- Asymptotically free scalar curvature-ghost coupling in Quantum Einstein Gravity
- Inflationary solutions in asymptotically safe f(R) theories
- The role of Background Independence for Asymptotic Safety in Quantum Einstein Gravity
- The Conformal Constraint in Canonical Quantum Gravity
- Fixed Points of Quantum Gravity and the Renormalisation Group
- The phase diagram of quantum gravity from diffeomorphism-invariant RG-flows
- Living with Infinities
- Limit cycles and quantum gravity