Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$

Abstract

We consider a particular large-radius limit of the worldsheet $S$-matrix for strings propagating on $Ad{S}_5\times S^5$. 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 ${\alpha }^{\prime }$ 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.

39 pages 5 figures; v2: Statement about singularities at $u_1-u_2=i$ corrected; v3: Typos, signs and coefficients corrected

References in corpus (3)

• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• Integrability and non-perturbative effects in the AdS/CFT correspondence

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• Gauge invariant finite size spectrum of the giant magnon
• Finite-Size Effects for Dyonic Giant Magnons
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• Aspects of Integrability in AdS/CFT Duality
• On the multi-spin magnon and spike solutions from membranes
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• Factorized Tree-level Scattering in AdS_4 x CP^3
• Giant Magnons and Spiky Strings on S^3 with B-field
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• Spin chain from membrane and the Neumann-Rosochatius integrable system
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• A note on the Near Flat Limit for strings in the Maldacena-Nunez background
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