Connecting giant magnons to the pp-wave: An interpolating limit of $AdS_5 \times S^5$

TL;DR

This paper explores a large-radius limit of the worldsheet S-matrix for strings on AdS5×S5, connecting the plane-wave and giant-magnon regimes, simplifying the model and analyzing the S-matrix's structure and consistency.

Contribution

It introduces a new interpolating limit of the worldsheet S-matrix that simplifies the theory and tests the proposed S-matrix against known regimes, providing insights into its analytic structure.

Findings

The limiting theory smoothly interpolates between plane-wave and giant-magnon regimes.

The proposed S-matrix reproduces expected results after Borel resummation.

Basic conclusions about the analytic structure of the S-matrix are drawn.

Abstract

We consider a particular large-radius limit of the worldsheet $S$-matrix for strings propagating on $AdS_5 \times S^5$. 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 non-trivial, and receives contributions to all orders in the $\alpha'$ expansion. We analyze a guess for the full worldsheet $S$ 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.