Related papers: Two-Loop Renormalization of a Chiral $SU(2)$ Gauge…
In this work we present a complete three-loop renormalisation of an abelian chiral gauge theory within the Breitenlohner-Maison/'t Hooft-Veltman (BMHV) scheme of dimensional regularisation (DReg). In this scheme the $\gamma_5$-matrix…
This thesis presents a comprehensive study of the renormalisation of chiral gauge theories in dimensional regularisation (DReg) at the multi-loop level. We employ the mathematically consistent Breitenlohner-Maison/`t~Hooft-Veltman (BMHV)…
We apply the BMHV scheme for non-anticommuting $\gamma_5$ to an abelian chiral gauge theory at the two-loop level. As our main result, we determine the full structure of symmetry-restoring counterterms up to the two-loop level. These…
$\gamma_5$ is notoriously difficult to define in $D$ dimensions. The traditional BMHV scheme employs a non-anticommuting $\gamma_5$. Its key advantage is mathematical consistency and the existence of all-order proofs. Its disadvantage is…
We present the complete 4-loop renormalisation of an Abelian chiral gauge theory in the Breitenlohner-Maison / `t Hooft-Veltman (BMHV) scheme. Employing a non-anticommuting $\gamma_5$ in dimensional regularisation, we determine the full set…
These proceedings discuss the current progress of the no-compromise approach to the dimensional renormalization of chiral gauge theories in the context of the BMHV scheme with non-anticommuting $\gamma_5$. Despite spuriously breaking…
We study the application of the Breitenlohner-Maison-'t Hooft-Veltman (BMHV) scheme of Dimensional Regularization to the renormalization of chiral gauge theories, focusing on the specific counterterm structure required by the…
This review provides a detailed introduction to chiral gauge theories, renormalization theory, and the application of dimensional regularization with the non-anticommuting BMHV scheme for $\gamma_5$. One goal is to show how chiral gauge…
It is known that the $\gamma_{5}$ scheme of Breitenlohner and Maison (BM) in dimensional regularization requires finite counter-term renormalization to restore gauge symmetry and implementing this finite renormalization in practical…
The mathematical consistency of the BMHV scheme of dimensional regularisation (DReg) comes at the cost of requiring symmetry-restoring counterterms to cancel the regularisation-induced breaking of gauge and BRST invariance. There is no…
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,…
The one-loop renormalization of a general chiral gauge theory without scalar and Majorana fields is fully worked out within Breitenlohner and Maison dimensional renormalization scheme. The coefficients of the anomalous terms introduced in…
Dimensional regularization is arguably the most popular and efficient scheme for multi-loop calculations. Yet, when applied to chiral (gauge) theories like the Standard Model and its extensions, one is forced to deal with the infamous…
The one-loop renormalization of the abelian Higgs-Kibble model in a general 't Hooft gauge and with chiral fermions is fully worked out within dimensional renormalization scheme with a non-anticommuting $\gamma_5$. The anomalous terms…
The two-loop anomalous dimension of the chiral matter superfields is calculated for a general ${\cal N}=1$ supersymmetric gauge theory regularized by higher covariant derivatives. We obtain both the anomalous dimension defined in terms of…
We present a systematic functional approach to calculating symmetry-restoring counterterms in Effective Field Theories (EFTs) regulated using the Breitenlohner--Maison--'t Hooft--Veltman (BMHV) scheme. Building on a recently developed…
We calculate the $10\times 10$ two--loop anomalous dimension matrix to order $\ord(\alpha_e \alpha_s)$ in the dimensional regularization scheme with anticommuting $\gamma_5$ (NDR) which is necessary for the extension of the $\Delta S=1$…
We adress ourselves the question of the quantum equivalence of non abelian dualised $\si$-models on the simple example of the T-dualised $SU(2) \si$-model. This theory is classically canonically equivalent to the standard chiral $SU(2)…
Anomalies and BRST invariance are governed, in the context of Lagrangian Batalin-Vilkovisky quantization, by the master equation, whose classical limit is $(S, S)=0$. Using Zimmerman's normal products and the BPHZ renormalisation method, we…
The nonlocal regularization method, recently proposed in ref.\,\ct{emkw91,kw92,kw93}, is extended to general gauge theories by reformulating it along the ideas of the antibracket-antifield formalism. From the interplay of both frameworks a…