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 is typically advertized.

Is there anything analogous to these results to be said about the light-cone quantization of the supermembrane in target space dimension 3+1 ?

  • $\begingroup$ as far as I know, unlike the superstring, there is no successful quantization of the super membrane. $\endgroup$ – Ali Moh Mar 18 '15 at 14:13

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