Vortex Loop Operators, M2-branes and Holography

TL;DR

This paper constructs and classifies supersymmetric vortex loop operators in a 3D Chern-Simons theory, linking them to M2-brane excitations in M-theory and describing their geometric duals in supergravity.

Contribution

It introduces a new class of BPS vortex loop operators in ABJM theory and connects them to M2-brane configurations and supergravity solutions.

Findings

Identified 1/2, 1/3, and 1/6 BPS vortex loop operators.

Mapped these operators to M2-branes ending on the boundary of AdS_4 x S^7/Z_k.

Provided a geometric description via bubbling supergravity solutions.

Abstract

We construct vortex loop operators in the three-dimensional N = 6 supersymmetric Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena. These disorder loop operators are specified by a vortex-like singularity for the scalar and gauge fields along a one dimensional curve in spacetime. We identify the 1/2, 1/3 and 1/6 BPS loop operators in the Chern-Simons theory with excitations of M-theory corresponding to M2-branes ending along a curve on the boundary of AdS_4 x S^7/Z_k. The vortex loop operators can also be given a purely geometric description in terms of regular "bubbling" solutions of eleven dimensional supergravity which are asymptotically AdS_4 x S^7/Z_k.