Decontracted double BRST on the lattice

TL;DR

This paper explores the lattice formulation of the Curci-Ferrari model with double BRST symmetry, showing how a mass term regulates the Neuberger 0/0 problem and analyzing the interplay of gauge parameters and mass.

Contribution

It introduces a lattice version of the Curci-Ferrari model with a mass term that regulates the Neuberger problem, extending the topological interpretation to include the ghost/anti-ghost symmetric formulation.

Findings

The mass term m decontracts the double BRST algebra, affecting unitarity.

Observables can be defined in the limit m to 0 using l'Hospital's rule.

The gauge parameter xi and mass m dependence cancel when appropriately adjusted.

Abstract

We present the Curci-Ferrari model on the lattice. In the massless case the topological interpretation of this model with its double BRST symmetry relates to the Neuberger 0/0 problem which we extend to include the ghost/anti-ghost symmetric formulation of the non-linear 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 to 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 xi and mass m dependence of the model and show how both cancel when m = m(xi) is appropriately adjusted with xi.