We consider a particular large-radius limit of the world sheet $S$ matrix for strings propagating on ${\mathrm{AdS}}_5\times S^5$. This limiting theory interpolates smoothly between the so-called plane-wave and giant-magnon regimes of the theory. The sigma model in this region simplifies; it stands as a toy model of the full theory, and may be easier to solve directly. The $S$ matrix of the limiting theory is nontrivial, and receives contributions to all orders in the ${\alpha }^{\prime }$ expansion. We analyze a guess for the full world sheet $S$ matrix that was formulated recently by Beisert, Hernandez, and Lopez, and Beisert, Eden, and Staudacher, and take the corresponding limit. After doing a Borel resummation we find that the proposed $S$ matrix reproduces the expected results in the giant-magnon region. In addition, we rely on general considerations to draw some basic conclusions about the analytic structure of the $S$ matrix.

• Received 19 March 2007

DOI:https://doi.org/10.1103/PhysRevD.76.026002