Finite size Giant Magnons in the string dual of N=6 superconformal Chern-Simons theory

TL;DR

This paper derives an exact finite-size Giant Magnon solution in the string dual of N=6 superconformal Chern-Simons theory, revealing finite-size effects on the magnon dispersion relation.

Contribution

It provides the first exact finite-size Giant Magnon solution in the SU(2)×SU(2) sector of the ABJM string dual, including finite-size exponential corrections.

Findings

Exact finite-size Giant Magnon solution found

Finite-size corrections to dispersion relation characterized

Solution reduces to known infinite size case

Abstract

We find the exact solution for a finite size Giant Magnon in the $SU(2)\times SU(2)$ sector of the string dual of the $\mathcal{N}=6$ superconformal Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena. The finite size Giant Magnon solution consists of two magnons, one in each $SU(2)$. In the infinite size limit this solution corresponds to the Giant Magnon solution of arXiv:0806.4959. The magnon dispersion relation exhibits finite-size exponential corrections with respect to the infinite size limit solution.