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In a previous work (arXiv:0902.3750 [hep-th]) we studied the world-sheetconformal invariance for superstrings in type IIB R-R plane-wave insemi-light-cone gauge. Here we give further justification to the results foundin that work through alternative arguments using dynamical supersymmetries. Weshow that by using the susy algebra the same quantum definition of theenergy-momentum (EM) tensor can be derived. Furthermore, using certain Jacobiidentities we indirectly compute the Virasoro anomaly terms by calculatingsecond order susy variation of the EM tensor. Certain integrated form of allsuch terms are shown to vanish. In order to deal with various divergences thatappear in such computations we take a point-split definition of the same EMtensor. The final results are shown not to suffer from the ordering ambiguityas noticed in the previous work provided the coincidence limit is taken beforesending the regularization parameter to zero at the end of the computation.

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