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.
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 ?-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 ?-function depends only on the universal details of the set-up, to all orders.
New Developments in the Continuous Renormalization Group
Over the last several years, there has been a resurgence of interest in using non-perturbative approximation methods based on Wilson's continuous renormalization group. In this lecture, I review progress particularly in the past year, concentrating on theoretical issues in the structure of the exact renormalization group and its approximations.