Supersymmetric null-surfaces

Single trace operators with the large R-charge in supersymmetric Yang-Mills theory correspond to the null-surfaces in $Ad{S}_5\times S^5$. We argue that the moduli space of the null-surfaces is the space of contours in the super-Grassmanian parametrizing the complex $(2\mathrm{\mid }2)$-dimensional subspaces of the complex $(4\mathrm{\mid }4)$-dimensional space. The odd coordinates on this super-Grassmanian correspond to the fermionic degrees of freedom of the superstring.