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

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