Common wisdom says that only the top dimensional part of the brane scan of GreenSchwarz super pbrane sigma models is quantum consistent (the critical strings and the Mbranes). But by the results in

Luca Mezincescu, Paul Townsend, Anyons from Strings, Phys.Rev.Lett.105:191601,2010 (arXiv:1008.2334)

Luca Mezincescu, Paul Townsend, Quantum 3D Superstrings, PhysRevD.84.106006 (arXiv:1106.1374)

Luca Mezincescu, Alasdair J. Routh, Paul Townsend, Equivalence of 3D Spinning String and Superstring(arXiv:1305.5049)
the GreenSchwarz superstring down in target space dimension 2+1 is at least more quantum consistent than common wisdom might suggest.
Is there anything analogous to these results to be said about the lightcone quantization of the membrane in target space dimension 3+1 ?