Supersymmetric null-surfaces

Abstract

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 $(2|2)$-dimensional subspaces of the complex $(4|4)$-dimensional space. The odd coordinates on this super-Grassmanian correspond to the fermionic degrees of freedom of the superstring.

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 3.2