Two-loop spectroscopy of short ABJM operators

We study the spectrum of anomalous dimensions of short operators in planar ABJM theory at two loops. Specifically we develop a method for solving the OSp(6|4) Bethe ansatz equations for a certain class of unpaired length-4 states with arbitrarily high number of excitations, and apply it to identify three new sequences of rational eigenvalues. Results for low-lying paired states in the OSp(4|2) sector are obtained by direct diagonalization of the spin chain Hamiltonian. We also study the SL(2|1) sector and identify the set of states that corresponds to the SL(2)-like Bethe ansatz of Gromov and Vieira. Finally we extend part of our analysis to length-6 operators.