Decontracted double BRST symmetry on the lattice

Abstract

We present the Curci-Ferrari model on the lattice. In the massless case the topological interpretation of this model with its double Becchi-Rouet-Stora-Tyutin (BRST) symmetry relates to the Neuberger $0/0$ problem which we extend to include the ghost/antighost symmetric formulation of the nonlinear-covariant Curci-Ferrari gauges on the lattice. The introduction of a Curci-Ferrari mass term, however, serves to regulate the $0/0$ indeterminate form of physical observables observed by Neuberger. While such a mass $m$ decontracts the double BRST/anti-BRST algebra, which is well known to result in a loss of unitarity, observables can be meaningfully defined in the limit $m\ensuremath{\rightarrow}0$ via l'Hospital's rule. At finite $m$, the topological nature of the partition function used as the gauge-fixing device seems lost. We discuss the gauge parameter $\ensuremath{\xi}$ and mass $m$ dependence of the model and show how both cancel when $m\ensuremath{\equiv}m(\ensuremath{\xi})$ is appropriately adjusted with $\ensuremath{\xi}$.