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

We introduce a family of new integrable quantum field theories in four dimensions by considering the γ-deformed N = 4 SYM in the double scaling limit of large imaginary twists and small coupling. This limit 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, and contain a wealth of conformal correlators such that the whole arsenal of AdS/CFT integrability remains applicable. As a special case of these models, we obtain a QFT of two complex scalars with a chiral, quartic interaction. The BMN vacuum anomalous dimension is dominated in each loop order by a single “wheel” graph, whose bulk represents an integrable “fishnet” graph. This explicitly demonstrates the all-loop integrability of gamma-deformed planar N=4 SYM, at least in our limit. Using this feature and integrability results we provided an explicit conjecture for the periods of double-wheel graphs with an arbitrary number of spokes in terms of multiple zeta values (MZV) of limited depth.