World-sheet scattering in AdS_5 x S^5 at two loops

TL;DR

This work analyzes world-sheet scattering in the near-flat-space limit of $AdS_5\times S^5$ to two loops. Using a reduced sigma-model with quartic interactions and a momentum-dependent coupling, the authors compute the two-loop dispersion correction and the complete two-loop S-matrix for the $su(2|2)\times su(2|2)$ symmetry, including the dressing phase. The results precisely agree with the near-flat limit of Beisert's conjectured S-matrix, providing a stringent perturbative check of the integrable structure. The findings highlight how Lorentz invariance is softly broken and recoverable via a boost-dependent rescaling, and they point toward higher-loop and non-perturbative avenues to further illuminate the AdS/CFT S-matrix.

Abstract

We study the AdS_5 x S^5 sigma-model truncated to the near-flat-space limit to two-loops in perturbation theory. In addition to extending previously known one-loop results to the full SU(2|2)^2 S-matrix we calculate the two-loop correction to the dispersion relation and then compute the complete two-loop S-matrix. The result of the perturbative calculation can be compared with the appropriate limit of the conjectured S-matrix for the full theory and complete agreement is found.

Figures (3)

• Figure 1: One-loop graphs. The basic structure for $s$, $t$ and $u$ channel graphs.
• Figure 2: Two-loop graphs. The first line shows the $s$-channel diagrams, the second line the $t$-channel and the last $u$-channel. To the diagrams in the first column, we refer to as "double bubble", to the second column as "wineglass" and to the third as "inverse wineglass".
• Figure 3: Loop diagrams