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An exactly solvable large $N$ model is constructed which reduces at low energies to the Standard Model plus the dimension six Higgs-gauge operators $g_1^2 H^\dagger H B_{\mu \nu} B^{\mu \nu}$, $g_2^2 H^\dagger H W^a_{\mu \nu} W^{a\mu \nu}$, $g_1 g_2 H^\dagger \tau^a H W^a_{\mu \nu} B^{\mu \nu}$, and $\epsilon^{abc} W^a_{\mu}{}^\nu W^b_{\nu}{}^\rho W^c_{\rho}{}^\mu$.
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