Y-system for γ-deformed ABJM theory

We investigate the integrable aspects of the planar $\gamma$-deformed ABJM theory and proposed the twisted asymptotic Bethe ansatz equations. A more general method through a twist generating functional was discussed, based on which, the asymptotic large L solution of Y-system is modified in order to match the asymptotic Bethe ansatz equations. Serval applications of our method were made in $sl(2)$ sector and some important examples in $\beta$-deformed ABJM were present as well.