S-duality and the giant magnon dispersion relation

TL;DR

This paper argues that the giant magnon dispersion relation in type IIB string theory remains non-renormalized due to S-duality, supported by strong coupling spectrum computations and symmetry considerations.

Contribution

It introduces a S-duality based argument for the non-renormalization of the giant magnon dispersion relation and computes the spectrum for (p,q)-strings at strong coupling.

Findings

Dispersion relation is non-renormalized due to S-duality.

Spectrum of (p,q)-strings computed at strong coupling.

Coupling dependence matches integrability-based conjectures.

Abstract

We use S-duality and planarity to propose an argument for the non-renormalization of the dispersion relation of giant magnon solutions in type IIB string theory on AdS_5 x S^5. We compute the spectrum of giant magnons for (p,q)-strings from field theory at strong coupling by using the central charge properties of electrically and magnetically charged supersymmetric states in the Coulomb branch of N=4 super Yang-Mills. We argue that the coupling dependence of the giant magnon dispersion relation conjectured in the literature using integrability assumptions is in fact the only functional dependence compatible with S-duality.