Scheme Independence to all Loops

TL;DR

This paper proves that in a gauge-invariant Exact Renormalization Group approach for SU(N) Yang-Mills, the perturbative beta function coefficients are independent of non-universal details like seed actions and covariantization, suggesting universality across schemes.

Contribution

It demonstrates that all explicit dependencies on non-universal choices cancel out in the perturbative beta function to all orders, highlighting scheme independence.

Findings

Beta function coefficients are scheme-independent to all orders.

Explicit dependence on seed action cancels out in the formalism.

Universality of the perturbative beta function is supported across schemes.

Abstract

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.