Abstract
We discuss the different forms of the functional RG equation and their relation to each other. In particular we suggest a generalized background field version that is close in spirit to the Polchinski equation as an alternative to the Wetterich equation to study Weinberg’s asymptotic safety program for defining quantum gravity, and argue that the former is better suited for this purpose. Using the heat kernel expansion and proper time regularization we find evidence in support of this program in agreement with previous work.
Highlights
An alternative to such a situation was proposed four decades ago by Weinberg [14, 15]
In particular we suggest a generalized background field version that is close in spirit to the Polchinski equation as an alternative to the Wetterich equation to study Weinberg’s asymptotic safety program for defining quantum gravity, and argue that the former is better suited for this purpose
In contrast the “asymptotic safety” (AS) program initiated by Weinberg if it can be realized in practice, should be able to calculate any gravitational process at arbitrarily high energies in terms of a finite number of parameters
Summary
∂gi ∂ ln Λ gives from as is well known, a set of equations for the beta functions βi In addition to this UV cutoff we will, in order to connect to the discussion of the so-called average effective action, introduce an infra-red (IR) cutoff k2. One needs to turn on the (marginally) relevant operator above at some large but finite cutoff Λ in order to flow away from the fixed point as one lowers the cutoff Λ. Even in this case the assumption that there is a meaningful Λ → ∞ action is invalid.
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