Regularization by dimensional reduction: Consistency, quantum action principle, and supersymmetry

Abstract

It is proven by explicit construction that regularisation by dimensional reduction can be formulated in a mathematically consistent way. In this formulation the quantum action principle is shown to hold. This provides an intuitive and elegant relation between the D-dimensional lagrangian and Ward or Slavnov-Taylor identities, and it can be used in particular to study to what extent dimensional reduction preserves supersymmetry. We give several examples of previously unchecked cases. © SISSA 2005.