Inelastic Magnon Scattering

TL;DR

This paper investigates the inelastic magnon scattering S-matrix in AdS/CFT, revealing boundstates, deriving crossing equations, and computing two-loop scattering to inform phase determination.

Contribution

It provides the first detailed analysis of inelastic magnon scattering, including boundstate poles, crossing equations, and two-loop results in the AdS/CFT context.

Findings

Identified poles corresponding to boundstates of magnons

Derived crossing equations for the overall phase

Computed two-loop scattering in the su(2) sector

Abstract

We study the worldsheet S-matrix of a string attached to a D-brane in AdS$_5\times$S$^5$. The D-brane is either a giant graviton or a dual giant graviton. In the gauge theory, the operators we consider belong to the $su(2|3)$ sector of the theory. Magnon excitations of open strings can exhibit both elastic (when magnons in the bulk of the string scatter) and inelastic (when magnons at the endpoint of an open string participate) scattering. Both of these $S$-matrices are determined (up to an overall phase) by the $su(2|2)^2$ global symmetry of the theory. In this note we study the $S$-matrix for inelastic scattering. We show that it exhibits poles corresponding to boundstates of bulk and boundary magnons. A crossing equation is derived for the overall phase. It reproduces the crossing equation for maximal giant gravitons, in the appropriate limit. Finally, scattering in the $su(2)$ sector is computed to two loops. This two loop result, which determines the overall phase to two loops, will be useful when a unique solution to the crossing equation is to be selected.