Regge trajectories and bridges between them in integrable AdS/CFT

We study the analytic continuation in the spin of the planar spectrum of ABJM theory using the integrability-based Quantum Spectral Curve (QSC) method. Under some minimal assumptions, we classify the analytic properties of the Q-functions appearing in the QSC compatible with the spin being non-integer. In this way we find not one - but $\textit{two}$ distinct possibilities. While one is related to standard Regge trajectories, we show that the second choice can be used to build bridges which connect leading and subleading Regge trajectories, thus giving a shortcut to reach infinitely many sheets of the spin Riemann surface without going explicitly around the branch points in the complex spin plane. Moreover, the bridges are exact spin reflections of standard Regge trajectories. Together, these results reveal the existence of a hidden symmetry which we call "twist/co-twist symmetry": every non-BPS local operator has an exact image - living below unitarity on a different Regge trajectory - with the same $\Delta$ and the spin flipped by a Weyl reflection. We discuss how an analogous phenomenon, based on the same mechanism at the level of the QSC, also occurs at non-perturbative level in $\mathcal{N}$$=$$4$ SYM. This provides a framework to understand recent independent observations of the symmetry in this model at weak and strong coupling. We present numerical results for Regge trajectories in planar ABJM theory, in particular we compute exactly the coupling dependence of the position of the leading Regge pole in the correlator of four stress tensors. The shape of this leading trajectory shows a behaviour at weak coupling that strongly resembles the BFKL limit in $\mathcal{N}$$=$$4$ SYM.