Giant magnons in the D1-D5 system

TL;DR

This paper investigates giant magnons in the D1-D5 system, demonstrating their BPS nature and periodic dispersion relation through both boundary CFT analysis and classical string solutions in $AdS_3\times S^3\times T^4$, revealing a deep algebraic structure.

Contribution

It identifies giant magnons as BPS states in an extended superalgebra and establishes their dispersion relation as periodic in momentum, unifying boundary and bulk descriptions.

Findings

Giant magnons are BPS states in a centrally extended superalgebra.

The dispersion relation for magnons is periodic in momentum.

The boundary CFT and string theory descriptions are consistent.

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