Integrable open spin chains from giant gravitons

TL;DR

This work studies open strings attached to a maximal giant graviton in $\mathcal{N}=4$ SYM by mapping to a $PSU(2,2|4)$ open spin chain in the $SO(6)$ sector at one loop. By computing planar anomalous dimensions and analyzing boundary scattering of defects, the authors derive the full boundary-influenced Hamiltonian and construct the boundary S-matrix, showing that the boundary Yang–Baxter equation holds. They find that boundary contributions vanish for $X,Y,\overline{X},\overline{Y}$ while $\overline{Z}$ (and $Z$) impose specific boundary conditions, leading to integrable open-chain dynamics. The results provide a controlled demonstration of integrability for open strings on maximal giant gravitons within AdS/CFT and set the stage for potential all-loop extensions and generalizations to orbifolds and more dynamic boundary configurations.

Abstract

We prove that in the presence of a maximal giant graviton state in N=4 SYM, the states dual to open strings attached to the giant graviton give rise to an PSU(2,2|4) open spin chain model with integrable boundary conditions in the SO(6) sector of the spin chain to one loop order.

Figures (2)

• Figure 1: Pictorial description of contractions leading to boundary conditions of the spin chain: The round boxes represent the determinant part of the operator, and the straight horizontal lines represent the spin chain part of the problem. Vertical lines indicate single contractions, and the thick vertical filled box represents the contractions of $Z,\bar{Z}$ between the determinant part of the operators.
• Figure 2: Pictorial representation of the Boundary Yang Baxter equation. The lines represent defects scattering from each other and the boundary (which is represented by the shaded region) in different orders.