  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 AdS(5)/CFT(4) 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 AdS(4)/CFT(3) spectrum.
