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1) The strong coupling expansion on the lattice is given in terms of [itex] \beta = N/g^2 [/itex].

But what is the other parameter of the lattice theory? Is it [itex]N[/itex]? In that case, does the [itex]\beta[/itex]-expansion break down at large-[itex]N[/itex] and large-[itex]g[/itex]?

2) Is there a direct continuum limit (at a physicist's rigor) of the strong-coupling lattice theory ie. a continuum theory constructed from Wilson line variables with coupling [itex]~1/g[/itex], rather than from fields coupling at [itex]g[/itex]?