Common wisdom says that only the top dimensional part of the brane scan of Green-Schwarz super p-brane sigma models is quantum consistent (the critical strings and the M-branes). 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 Green-Schwarz 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 light-cone quantization of the membrane in target space dimension 3+1 ?