Massless sector of ${\mathrm{AdS}}_3$ superstrings: A geometric interpretation

We study the recently discovered $q$-deformed Poincaré supersymmetry of the ${\mathrm{AdS}}_3/{\mathrm{CFT}}_2$ integrable massless scattering, and demonstrate how the $S$-matrix is invariant under boosts. The boost generator has a nonlocal 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 Schrödinger problem. We support our claims by performing a simplified algebraic Bethe ansatz, which bears some resemblance to antiferromagnets.