1306.1223 (Juergen A. Dietz et al.)

Redundant operators in the exact renormalisation group and in the f(R)
approximation to asymptotic safety    [PDF]

Juergen A. Dietz, Tim R. Morris

In this paper we review the definition and properties of redundant operators in the exact renormalisation group. We then apply this to the Local Potential Approximation and approximations of a similar spirit such as the f(R) approximation in the asymptotic safety programme in quantum gravity. We show that these approximations can break down if the fixed point does not support a `vacuum' solution in the appropriate domain: all eigenoperators become redundant and the physical space of perturbations collapses to a point. We show that this is the case for the recently discovered lines of fixed points in the f(R) flow equations. In contrast, although earlier versions of the f(R) flow equations do not have globally well defined fixed point solutions, we show that the partial solution picked out by high order truncations, does support a `vacuum' solution in the appropriate domain. As a consequence in this latter case none of the eigenoperators are redundant.

View original: http://arxiv.org/abs/1306.1223