Relationships Between Exact RGs and some Comments on Asymptotic Safety

Abstract

The standard flow equation for the effective average action can be derived from a Legendre transform of Polchinski's exact renormalization group equation. However, the latter is not well adapted for finding fixed-points with non-zero anomalous dimension. Instead, it is more convenient to use a modified version which ensures that the redundant coupling associated with the normalization of the field never appears in the action. Taking this as the starting point, a Legendre transform is constructed allowing a direct derivation of the corresponding flow equation for the effective average action. This equation is then used to exactly construct some illuminating though essentially trivial) asymptotically safe trajectories emanating from various non-unitary fixed-points. Finally, in the context of asympotically safe quantum gravity, it is pointed out that the standard argument that the anomalous dimension of Newton's constant is necessarily 2-d at a non-trivial fixed-point is incomplete. The implications of this are discussed.

8 pages

References in corpus (6)

• Nonperturbative Evolution Equation for Quantum Gravity
• Flow Equation of Quantum Einstein Gravity in a Higher-Derivative Truncation
• Elements of the Continuous Renormalization Group
• Ghost anomalous dimension in asymptotically safe quantum gravity
• Evidence for Asymptotic Safety from Lattice Quantum Gravity
• Equivalent Fixed-Points in the Effective Average Action Formalism

Cited by in corpus (7)

• Essential Quantum Einstein Gravity
• BRST in the Exact RG
• RG flow equations for the proper-vertices of the background effective average action
• A Conformal Fixed-Point Equation for the Effective Average Action
• Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety
• Structure of Exact Renormalization Group Equations for field theory
• On the wave function renormalization for Wilson actions and their 1PI actions