Abstract
It is shown that self-duality of gauge theories in the large-N limit when g2N is kept finite extends to an invariance under the full modular group in parameter space when a theta -term is included. The author suggests using modular covariant combinations of modular forms to construct the generating functional in the large-N limit. This fixes the phase transitions to be on the boundaries of the horocircles defining the fundamental domain of the modular group.
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