Quantum Scattering of Giant Magnons

TL;DR

This work computes the one-loop semiclassical corrections to both the dispersion and S-matrix of Giant Magnons in $AdS_{5}\times S^{5}$, and finds exact agreement with the strong-coupling expansion of the exact ABAE, notably reproducing the Hernandez-Lopez term in the dressing phase. It achieves this through three complementary methods — dressing method, finite-gap analysis, and a consistency check based on the ${\mathfrak{su}}(2|2)$ S-matrix — to extract classical phase shifts of fluctuations and then apply standard one-loop formulas. The main results are that the soliton energy has vanishing one-loop correction ($\Delta E(p)=0$) and that the one-loop correction to the S-matrix, $\Delta\Theta(p_1,p_2)$, matches the HL contribution, thereby confirming ABAE predictions and the universality of HL in semiclassical string theory. Overall, the paper strengthens the link between integrability-based predictions and explicit semiclassical string computations, reinforcing the role of HL-type corrections in the AdS/CFT correspondence.

Abstract

We perform a first-principles semi-classical computation of the one-loop corrections to the dispersion relation and S-matrix of Giant Magnons in AdS_5 x S^5 string theory. The results agree exactly with expectations based on the strong coupling expansion of the exact Asymptotic Bethe Ansatz equations. In particular we reproduce the Hernandez-Lopez term in the dressing phase.

Figures (2)

• Figure 1: The one-soliton solution at time $t=0$.
• Figure 2: The two-soliton scattering solution at time $t=0$.