Dynamical supersymmetry analysis of conformal invariance for superstrings in type IIB RR plane-wave background

In a previous work (arXiv:0902.3750 [hep-th]) we studied the world-sheet conformal invariance for superstrings in the type IIB R-R plane-wave in semi-light-cone gauge. Here we give further justification to the results found in that work through alternative arguments using dynamical supersymmetries. We show that by using the supersymmetry algebra the same quantum definition of the energy-momentum (EM) tensor can be derived. Furthermore, using certain Jacobi identities we indirectly compute the Virasoro anomaly terms by calculating the second-order supersymmetry variation of the EM tensor. Certain integrated forms of all such terms are shown to vanish. In order to deal with various divergences that appear in such computations we take a point-split definition of the same EM tensor. The final results are shown not to suffer from the ordering ambiguity as noticed in the previous work provided the coincidence limit is taken before sending the regularization parameter to zero at the end of the computation.