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Nearly all gauge-fixing prescriptions are based upon setting some function involving the gauge fields to be zero. That function is continuous and varies over the real/complex numbers. Trying the same trick for discrete gauge symmetries break down because we have no continuity, and hence, no implicit function theorem.

So are there any good prescriptions out there?

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The axial gauges work fine for discrete and continuous gauges both. You just declare that the gauge field in one direction, say the x-direction, is zero. This means that the discrete/continuous parallel transport is the identity when you take horizontal steps.

You don't need to gauge fix over discrete gauge symmetries, just sum over the gauge equivalent configurations, it doesn't do any harm. Even for continuous gauge symmetry, you don't gauge fix on a lattice, because the gauge group volume is locally finite. You just sum over gauge equivalent configurations, it's not a problem.

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Small typos : the gauge fields in one direction, [...], is zero -> the gauge potentials in one direction ... – FraSchelle Feb 9 at 12:10

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