6 research outputs found

### Scheme Independence to all Loops

The immense freedom in the construction of Exact Renormalization Groups means
that the many non-universal details of the formalism need never be exactly
specified, instead satisfying only general constraints. In the context of a
manifestly gauge invariant Exact Renormalization Group for SU(N) Yang-Mills, we
outline a proof that, to all orders in perturbation theory, all explicit
dependence of beta function coefficients on both the seed action and details of
the covariantization cancels out. Further, we speculate that, within the
infinite number of renormalization schemes implicit within our approach, the
perturbative beta function depends only on the universal details of the setup,
to all orders.Comment: 18 pages, 8 figures; Proceedings of Renormalization Group 2005,
Helsinki, Finland, 30th August - 3 September 2005. v2: Published in jphysa;
minor changes / refinements; refs. adde

### Sensitivity of Nonrenormalizable Trajectories to the Bare Scale

Working in scalar field theory, we consider RG trajectories which correspond
to nonrenormalizable theories, in the Wilsonian sense. An interesting question
to ask of such trajectories is, given some fixed starting point in parameter
space, how the effective action at the effective scale, Lambda, changes as the
bare scale (and hence the duration of the flow down to Lambda) is changed. When
the effective action satisfies Polchinski's version of the Exact
Renormalization Group equation, we prove, directly from the path integral, that
the dependence of the effective action on the bare scale, keeping the
interaction part of the bare action fixed, is given by an equation of the same
form as the Polchinski equation but with a kernel of the opposite sign. We then
investigate whether similar equations exist for various generalizations of the
Polchinski equation. Using nonperturbative, diagrammatic arguments we find that
an action can always be constructed which satisfies the Polchinski-like
equation under variation of the bare scale. For the family of flow equations in
which the field is renormalized, but the blocking functional is the simplest
allowed, this action is essentially identified with the effective action at
Lambda = 0. This does not seem to hold for more elaborate generalizations.Comment: v1: 23 pages, 5 figures, v2: intro extended, refs added, published in
jphy

### Conformal anomaly from gauge fields without gauge fixing

We show how the Weyl anomaly generated by gauge fields, can be computed from
manifestly gauge invariant and diffeomorphism invariant exact renormalization
group equations, without having to fix the gauge at any stage. Regularisation
is provided by covariant higher derivatives and by embedding the Maxwell field
into a spontaneously broken $U(1|1)$ supergauge theory. We first provide a
realisation that leaves behind two versions of the original $U(1)$ gauge field,
and then construct a manifestly $U(1|1)$ supergauge invariant flow equation
which leaves behind only the original Maxwell field in the spontaneously broken
regime.Comment: 24 page