Supersymmetric null-surfaces

Single trace operators with the large R-charge in supersymmetric Yang-Millstheory correspond to the null-surfaces in $AdS_5\times S^5$. We argue that themoduli space of the null-surfaces is the space of contours in thesuper-Grassmanian parametrizing the complex $(2|2)$-dimensional subspaces ofthe complex $(4|4)$-dimensional space. The odd coordinates on thissuper-Grassmanian correspond to the fermionic degrees of freedom of thesuperstring.Comment: v4: added a reference to the earlier work; corrected the formula for the stabilizer of the BMN vacuum; added the discussion of the complex structure of the odd coordinates in Section 3.