Renormalisation of general N=2 supersymmetric Chern-Simons theories in three dimensions

We present exact results for the Beta-functions for the soft-breaking parameters in softly-broken N = 2 Chern-Simons matter theories in terms of the anomalous dimension in the unbroken theory. We check our results explicitly up to the two loop level. We then go on to present results for the planar contribution to the four-loop anomalous dimension for a general N = 2 supersymmetric Chern-Simons theory in three dimensions. These results should facilitate higher-order superconformality checks for theories relevant for the AdS/CFT correspondence. We then go on to discuss possible higher-loop corrections to superconformal invariance for a class of N = 2 supersymmetric Chern-Simons theories including the ABJM model. We argue that corrections are inevitable even for simple generalisations of the ABJM model; but that it is likely that any corrections are of a particular "maximally transcendental" form