Renormalisation Group Equations for BRST-Restored Chiral Theory in Dimensional Renormalisation: Application to Two-Loop Chiral-QED

TL;DR

This paper develops and compares renormalisation group equations for a chiral quantum field theory with restored BRST symmetry using algebraic renormalisation in dimensional regularisation, applied to two-loop chiral-QED.

Contribution

It introduces a consistent formulation of RG equations in a BRST-restored chiral theory within the BMHV scheme, comparing algebraic and multiplicative renormalisation methods.

Findings

Beta-functions computed up to two loops.

Anomalous dimensions evaluated at two-loop order.

Algebraic renormalisation effectively restores BRST symmetry.

Abstract

We discuss how renormalisation group equations can be consistently formulated using the algebraic renormalisation framework, in the context of a dimensionally-renormalised chiral field theory in the BMHV scheme, where the BRST symmetry, originally broken at the quantum level, is restored via finite counterterms. We compare it with the more standard multiplicative renormalisation approach, which application would be more cumbersome in this setting. Both procedures are applied and compared on the example of a massless chiral right-handed QED model, and beta-function and anomalous dimensions are evaluated up to two-loop orders.