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We compute the null cusp anomalous dimension of ABJM theory at strongcoupling up to two-loop order. This is done by evaluating corrections to thecorresponding superstring partition function, weighted by the $AdS_4\times\mathbb{CP}^3$ action in AdS light-cone gauge. We compare our result, where weuse an anomalous shift in the $AdS_4$ radius, with the cusp anomaly of$\mathcal{N}=4$ SYM, and extract the two-loop contribution to the non-trivialintegrable coupling $h(\lambda)$ of ABJM theory. It coincides with the strongcoupling expansion of the exact expression for $ h(\lambda)$ recentlyconjectured by Gromov and Sizov. Our work provides thus a non-trivialperturbative check for the latter, as well as evidence for two-loopUV-finiteness and quantum integrability of the Type IIA $AdS_4\times\mathbb{CP}^3$ superstring in this gauge.

Two-loop cusp anomaly in ABJM at strong coupling