Giant magnons in the D1-D5 system

TL;DR

This work analyzes giant magnons in the D1-D5 system from both the boundary CFT and classical string theory on $AdS_3\times S^3\times T^4$. It uncovers a centrally extended $SU(1|1)\times SU(1|1)$ algebra with two extra central charges governing magnons, yielding a dispersion $\Delta-J = \sqrt{1 + f(\tilde{\lambda})\sin^{2}(p/2)}$ that matches perturbative and classical results. At weak coupling, $f(\tilde{\lambda}) = \lambda^{2}Q_1Q_5/\pi^{2}$, while at strong coupling the same form is reproduced with $f(\tilde{\lambda}) \to g_6^{2}Q_1Q_5/\pi^{2}$, realized by a classical stretched-string magnon in $AdS_3\times S^3$. The paper also develops a dynamic spin-chain representation and demonstrates that the giant magnon preserves supersymmetry, providing a foundation for potential integrability and S-matrix construction in this holographic setup.

Abstract

We study giant magnons in the the D1-D5 system from both the boundary CFT and as classical solutions of the string sigma model in $AdS_3\times S^3\times T^4$. Re-examining earlier studies of the symmetric product conformal field theory we argue that giant magnons in the symmetric product are BPS states in a centrally extended $SU(1|1)\times SU(1|1)$ superalgebra with two more additional central charges. The magnons carry these additional central charges locally but globally they vanish. Using a spin chain description of these magnons and the extended superalgebra we show that these magnons obey a dispersion relation which is periodic in momentum. We then identify these states on the string theory side and show that here too they are BPS in the same centrally extended algebra and obey the same dispersion relation which is periodic in momentum. This dispersion relation arises as the BPS condition for the extended algebra and is similar to that of magnons in ${\cal N}=4$ Yang-Mills