Discontinuity relations for the AdS4/CFT3 correspondence

We study in detail the analytic properties of the Thermodynamic Bethe Ansatz (TBA) equations for the anomalous dimensions of composite operators in the planar limit of the 3D N=6 superconformal Chern-Simons gauge theory and derive functional relations for the jump discontinuities across the branch cuts in the complex rapidity plane. These relations encode the analytic structure of the Y functions and are extremely similar to the ones obtained for the previously-studied AdS5/CFT4 case. Together with the Y-system and more basic analyticity conditions, they are completely equivalent to the TBA equations. We expect these results to be useful to derive alternative nonlinear integral equations for the AdS4/CFT3 spectrum.