Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory

TL;DR

This work analyzes the spin-chain description of the ${\cal N}=6$ Chern-Simons-matter theory (ABJM) and its AdS$_4\times\mathbb{CP}^3$ dual, focusing on non-BPS sectors. By computing the two-loop dilatation operator in subsectors and studying the centrally extended $SU(2|2)$ algebra, the authors derive exact dispersion relations and scattering data for spin-chain impurities, and reveal a structure that matches string-theory expectations in the Penrose limit. They show that the $SU(2)_A\times SU(2)_B$ sector comprises two decoupled XXX spin-$\tfrac12$ chains, while the infinite chain hosts a central charge $Z=f(\lambda)(1-e^{2\pi i P})$ with a coupling-dependent function $f(\lambda)$, displaying different weak and strong coupling scalings. The Penrose-limit analysis yields a pp-wave spectrum with masses $1$ and $1/2$ and dispenses dispersion relations $E^{(i)} = \sqrt{1+2\lambda(\pi p)^2}$ and $E^{(j)} = \sqrt{1/4+2\lambda(\pi p)^2}$, sharpening the connection between gauge theory integrability and string dynamics. Finally, giant-magnon solutions on $AdS_4\times\mathbb{CP}^3$ are described, including a CP$^1$ magnon with $E-J$ scaling as $\sqrt{2\lambda}$ and an RP$^2$ magnon, highlighting subtleties in matching gauge and string pictures and the potential role of fermionic zero modes.

Abstract

In this note we study spin chain operators in the N=6 Chern-Simons-matter theory recently proposed by Aharony, Bergman, Jafferis and Maldacena to be dual to type IIA string theory in AdS4xCP3. We study the two-loop dilatation operator in the gauge theory, and compare to the Penrose limit on the string theory side.