Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation

By Martin Reuter, Frank Saueressig. 2001

450 citations recorded by the source corpus.

The exact renormalization group equation for pure quantum gravity is used to derive the nonperturbative \ensuremath{\beta}-functions for the dimensionless Newton constant and cosmological constant on the theory space spanned by the Einstein-Hilbert truncation. The resulting coupled differential equations are evaluated for a sharp cutoff function. The features of these flow equations are compared to those found when using a smooth cutoff. The system of equations with a sharp cutoff is then solved numerically, deriving the complete renormalization group flow of the Einstein-Hilbert truncation in $d=4.$ The resulting renormalization group trajectories are classified and their physical relevance is discussed. The nontrivial fixed point which, if present in the exact theory, might render quantum Einstein gravity nonperturbatively renormalizable is investigated for various spacetime dimensionalities.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a530fc8acf369dba2a0dd267d7b8aac77732512b

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Citations in the corpus

QED coupled to QEG (2011, methodology): “We can therefore classify the trajectories as in [ 25 ], being of type Ia, IIa, and IIIa, when the IR value of the cosmological constant is negative, zero, or positive, respectively.”
Dimension and dimensional reduction in quantum gravity (2017, background): “The asymptotic safety program offers a fascinating possibility for the quantization of gravity, starkly different from other, more common approaches, such as string theory and loop quantum gravity [1–3].”
An Asymptotically Safe Guide to Quantum Gravity and Matter (2018, background): “Considerable evidence for the existence of the interacting Reuter fixed point has accumulated, starting from the seminal work (Dou and Percacci, 1998; Reuter, 1998; Souma, 1999; Lauscher and Reuter, 2002; Reuter and Saueressig, 2002), employing truncations of the form”
The nonperturbative functional renormalization group and its applications (2020, methodology): “Figure 26: The RG flow in a) the Einstein-Hilbert truncation from [1071], b) the Einstein-Hilbert truncation plus a curvature-cubed term from [1085] and c) in the reverse direction (i.”
Nonperturbative properties of Yang–Mills theories (2018, unknown): “, [108–119], Higgs physics, e.”