Massless sector of AdS_3 superstrings: a geometric interpretation

Abstract

We study the recently discovered q-deformed Poincare' supersymmetry of the AdS_3/CFT_2 integrable massless scattering, and demonstrate how the S-matrix is invariant under boosts. The boost generator has a non-local coproduct, which acts on the scattering matrix as a differential operator, annihilating it. We propose to reinterpret the boost action in terms of covariant derivatives on bundles, and derive an expression for the S-matrix as the path-ordered exponential of a flat connection. We provide a list of possible alternative interpretations of this emergent geometric picture, including a one-dimensional auxiliary Schroedinger problem. We support our claims by performing a simplified algebraic Bethe ansatz, which bears some resemblance to antiferromagnets.

arXiv commentREVTeX, 9 pages; no figures; v2: references added; v3: typo corrected

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• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• Nonlocal Symmetries, Spectral Parameter and Minimal Surfaces in AdS/CFT
• Massless $Ad{S}_2$ scattering and Bethe ansatz
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• A study of integrable form factors in massless relativistic AdS_3
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• Geometry of Massless Scattering in Integrable Superstring
• Complex D($2,1;\zeta$) and spin chain solutions from Chern-Simons theory