Supersymmetric null-surfaces

TL;DR

This paper explores the geometric structure of null-surfaces in supersymmetric string theory, linking them to super-Grassmanians and their fermionic degrees of freedom, providing a new mathematical framework for understanding supersymmetric null-surfaces.

Contribution

It introduces a novel description of the moduli space of supersymmetric null-surfaces as contours in a super-Grassmanian, connecting string fermionic modes with geometric structures.

Findings

Moduli space of null-surfaces is the space of contours in super-Grassmanian.

Odd coordinates on super-Grassmanian correspond to fermionic string degrees of freedom.

Provides a geometric framework for supersymmetric null-surfaces in AdS/CFT context.

Abstract

Single trace operators with the large R-charge in supersymmetric Yang-Mills theory correspond to the null-surfaces in $AdS_5\times S^5$. 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.