A Gauge-Fixing Action for Lattice Gauge Theories

We present a lattice gauge-fixing action $S_{gf}$ with the following properties: (a) $S_{gf}$ is proportional to the trace of $(\sum_\mu \partial_\mu A_\mu)^2$,plusirrelevanttermsofdimensionsixandhigher;(b)$S_{gf}$hasauniqueabsoluteminimumat$U_{x,\mu}=I$. Noting that the gauge-fixed action is not BRST invariant on the lattice, we discuss some important aspects of the phase diagram.