Mapping between $\gamma_5$ schemes in the Standard Model Effective Field Theory

We explore the relation between two distinct prescriptions for $\gamma_5$ in dimensional regularization -- the Breitenlohner Maison t'Hooft Veltman (BMHV) scheme and Naive Dimensional Regularisation (NDR). The BMHV scheme is the only algebraically consistent scheme, but necessitates chiral symmetry restoring counterterms and it is computationally more expensive, limiting its practical use. We show how the quantum effective action can be translated between both schemes and present these translation rules for the Wilson Coefficients of the Standard Model Effective Field Theory (SMEFT), that can easily be implemented into automated tools for SMEFT computations. Finally, we examine how this scheme dependence manifests itself in matching calculations, identifying the cases in which the dependence cancels in the final result. To examplify this, we consider a concrete UV scenario matched onto the SMEFT at one-loop order in both schemes. Our work aims to facilitate more accurate SMEFT computations and can be considered as a first step towards a comprehensive map between the two continuation schemes.