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Abstract: Geometric picture of line operators of N = 2 class S theories was found by imposing closure condition on operator product expansion (OPE) of line operators. In this paper, we first identify the geometric representation of ordinary Wilson-’t Hooft line operators of field theory, and study duality action on them. We further define a Dirac product between line operators and classify the allowed set of line operators by requiring: a: closure of OPE; b: mutual locality; c: maximality. Using above classifications, we find many distinct gauge theories associated with a single duality frame, and show explicitly that new possibilities correspond to the choice of global form of gauge group and discrete θ angles. We also study S and T duality actions relating those theories. In particular, we find very interesting duality webs for Maldacena-Nunez theory. ar X i