Large J expansion in ABJM theory revisited

Recently there has been progress in the computation of the anomalous dimensions of gauge theory operators at strong coupling by making use of AdS/CFT correspondence. On string theory side they are given by dispersion relations in the semiclassical regime. We revisit the problem of large charges expansion of the dispersion relations for simple semiclassical strings in $AdS_4\times\mathbb{CP}^3$ background. We present the calculation of the corresponding anomalous dimensions of the gauge theory operators to an arbitrary order using three different methods. Although the results of the three methods look different, power series expansions show their consistency.