BPS operators from the Wilson loop in the 3-dimensional supersymmetric Chern-Simons theory

TL;DR

This paper explores how small deformations of a Wilson loop in 3D superconformal Chern-Simons theory produce BPS operators that correspond to excited string states in the dual IIA string theory, revealing the interplay between gauge theory and string theory.

Contribution

It introduces a method to derive BPS operators from Wilson loop deformations in 3D superconformal Chern-Simons theory, linking them to string excitations.

Findings

BPS operators are obtained via Taylor expansion of Wilson loops.

BPS conditions constrain loop variables and operators.

Connection established between gauge theory operators and string states.

Abstract

We consider the small deformation of the point-like Wilson loop in the 3-dimensional $\mathcal{N}=6$ superconformal Chern-Simons theory. By Taylor expansion of the point-like Wilson loop in powers of the loop variables, we obtain the BPS operators that correspond to the excited string states of the dual IIA string theory on the pp wave background. The BPS conditions of the Wilson loop constrain both the loop variables and the forms of the operators obtained in the Taylor expansion.