16 research outputs found
Background independent exact renormalization group for conformally reduced gravity
Within the conformally reduced gravity model, where the metric is
parametrised by a function of the conformal factor , we keep
dependence on both the background and fluctuation fields, to local potential
approximation and respectively, making no other
approximation. Explicit appearances of the background metric are then dictated
by realising a remnant diffeomorphism invariance. The standard non-perturbative
Renormalization Group (RG) scale is inherently background dependent, which
we show in general forbids the existence of RG fixed points with respect to
. By utilising transformations that follow from combining the flow equations
with the modified split Ward identity, we uncover a unique background
independent notion of RG scale, . The corresponding RG flow equations
are then not only explicitly background independent along the entire RG flow
but also explicitly independent of the form of . In general is
forced to be scale dependent and needs to be renormalised, but if this is
avoided then -fixed points are allowed and furthermore they coincide with
-fixed points.Comment: 53 pages, broken reference correcte
Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety
In this paper we review the definition and properties of redundant operators in the exact renormalisation group. We explain why it is important to require them to be eigenoperators and why generically they appear only as a consequence of symmetries of the particular choice of renormalisation group equations. This clarifies when Newton’s constant and or the cosmological constant can be considered inessential. We then apply these ideas 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
Asymptotic safety in the f(R) approximation
In the asymptotic safety programme for quantum gravity, it is important to go
beyond polynomial truncations. Three such approximations have been derived
where the restriction is only to a general function f(R) of the curvature R>0.
We confront these with the requirement that a fixed point solution be smooth
and exist for all non-negative R. Singularities induced by cutoff choices force
the earlier versions to have no such solutions. However, we show that the most
recent version has a number of lines of fixed points, each supporting a
continuous spectrum of eigen-perturbations. We uncover and analyse the first
five such lines. Sensible fixed point behaviour may be achieved if one
consistently incorporates geometry/topology change. As an exploratory example,
we analyse the equations analytically continued to R<0, however we now find
only partial solutions.We show how these results are always consistent with,
and to some extent can be predicted from, a straightforward analysis of the
constraints inherent in the equations.Comment: Latex, 66 pages, published version, typos correcte
The local potential approximation in the background field formalism
Working within the familiar local potential approximation, and concentrating
on the example of a single scalar field in three dimensions, we show that the
commonly used approximation method of identifying the total and background
fields, leads to pathologies in the resulting fixed point structure and the
associated spaces of eigenoperators. We then show how a consistent treatment of
the background field through the corresponding modified shift Ward identity,
can cure these pathologies, restoring universality of physical quantities with
respect to the choice of dependence on the background field, even within the
local potential approximation. Along the way we point out similarities to what
has been previously found in the f(R) approximation in asymptotic safety for
gravity.Comment: 40 pages, version accepted by JHE