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We consider the $\gamma$-deformed $\mathcal{N}=4$ SYM in the double scalinglimit of large imaginary twists and small coupling, which discards the gaugefields and retains only certain Yukawa and scalar interactions with threearbitrary effective couplings. In the 't~Hooft limit, these 4D theories areintegrable, with most of the correlators being conformal such that the wholearsenal of AdS/CFT integrability remains applicable. In particular, for onenon-zero effective coupling, we obtain a QFT of two complex scalars with achiral, quartic interaction. The BMN vacuum anomalous dimension is dominated ineach non-zero loop order by a single "wheel" graph, in principle computable byintegrability. Thus we also provide an explicit conjecture for the periods ofdouble-wheel graphs with an arbitrary number of spokes.

New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM