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We study the phase diagram of $q$-deformed Yang-Mills theory on $S^2$ atnon-zero $\theta$-angle using the exact partition function at finite $N$. Byevaluating the exact partition function numerically, we find evidence for theexistence of a series of phase transitions at non-zero $\theta$-angle asconjectured in [hep-th/0509004].

Phase diagram of $q$-deformed Yang-Mills theory on $S^2$ at non-zero $\theta$-angle