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$\gamma_5$ 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…
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)…
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…
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…
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…
We outline the evaluation of $n$-dimensional fermion traces ($n\in\mathbb{N}$) built by products of Dirac-$\gamma$ matrices suitable for a uniform dimensional continuation. Such a continuation is needed for calculations employing a…
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…
Higher order calculations in chiral gauge theories such as the Electroweak Standard Model require a sound treatment of the notoriously problematic $\gamma_5$-matrix in Dimensional Regularization (DReg). In the all-order consistent BMHV…
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…
We investigate the trace anomaly of a chiral fermion in dimensional regularization, considering in detail the simplest case of coupling to an abelian gauge field. We apply the Breitenlohner-Maison/'t Hooft-Veltman prescription for dealing…
In the present paper we evaluate the anomaly for the abelian axial current in a non abelian chiral gauge theory, by using dimensional regularization. This amount to formulate a procedure for managing traces with more than one $\gamma_5$.…
We study dimensional reduction of M5 branes on a circle bundle when the supersymmetry parameter is not constant along the circle. When the gauge group is Abelian and the fields appear quadratically in the Lagrangian, we can always obtain a…
We present a method to perform renormalized perturbation calculation in gauge theories with chiral fermions. We find it proper to focus directly on the Ward-Takahashi identities, relegating dimensional regularization into a supplementary…
We propose a treatment of $\gamma^5$ in dimensional regularization which is based on an algebraically consistent extension of the Breitenlohner-Maison-'t Hooft-Veltman (BMHV) scheme; we define the corresponding minimal renormalization…
We consider regularisation of a Yang-Mills theory by Dimensional Reduction (DRED). In particular, the anomalous dimensions of fermion masses and gauge coupling are computed to four-loop order. We put special emphasis on the treatment of…
The Standard Model calculation of $H\rightarrow\gamma\gamma$ has the curious feature of being finite but regulator-dependent. While dimensional regularization yields a result which respects the electromagnetic Ward identities, additional…
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…
I formulate a deformation of the dimensional-regularization technique that is useful for theories where the common dimensional regularization does not apply. The Dirac algebra is not dimensionally continued, to avoid inconsistencies with…
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…
For some years there has been uncertainty over whether regularisation by dimensional reduction (DRED) is viable for non-supersymmetric theories. We resolve this issue by showing that DRED is entirely equivalent to standard dimensional…