Entropic order parameters in weakly coupled gauge theories

The entropic order parameters measure in a universal geometric way the statistics of non-local operators responsible for generalized symmetries. In this article, we compute weakly coupled gauge theories. To perform computation, natural route evaluating expectation values physical (smeared) is prevented by known difficulties constructing suitable smeared Wilson loops. We circumvent problem studying class enlarged non-gauge invariant Hilbert space. This provides generic approach theories and explicit formulas at weak coupling. approach, 't Hooft loops are labeled full weight co-weight lattices respectively. study Lie groups discuss couplings with matter fields. Smeared magnetic operators, as opposed to usual infinitely thin ones, have that one corresponding parameter saturates its maximum topological value, except an exponentially small correction, which compute. On other hand, their disorder small. verify both behaviors match certainty relation relative entropies. particular, find upper lower bounds (that differ factor 2) exact coefficient linear perimeter law unphysical/non-universal line operators. end some comments regarding RG flows through perturbative beta functions.