Konishi anomaly and central extension in N=12 supersymmetry

We show that the 4-dimensional N=1/2 supersymmetry algebra admits central extension. The central charges are supported by a domain wall and the central charges are computed. We also determine the Konishi anomaly for N=1/2 supersymmetric gauge theory. Due to the new couplings in the Lagrangian, many terms appear. We show that these terms sum up to give the expected form for the holomorphic part of the Konishi anomaly. For the antiholomorphic part, we give a simple argument that the naive generalization has to be modified. We suggest that the antiholomorphic Konishi anomaly is given by a gauge invariant completion using the open Wilson line.