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Massless sector of ${AdS}_{3}$ superstrings: A geometric interpretation

Andrea Fontanella^* and Alessandro Torrielli^†

Department of Mathematics, University of Surrey, Guildford GU2 7XH, United Kingdom

^*a.fontanella@surrey.ac.uk
^†a.torrielli@surrey.ac.uk

Phys. Rev. D 94, 066008 – Published 21 September, 2016

DOI: https://doi.org/10.1103/PhysRevD.94.066008

Abstract

We study the recently discovered $q$ -deformed Poincaré 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 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.

Physics Subject Headings (PhySH)

Integrability in field theory

Article Text

References (52)

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Massless sector of ${AdS}_{3}$ superstrings: A geometric interpretation

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Massless sector of AdS3 superstrings: A geometric interpretation

Abstract

Physics Subject Headings (PhySH)

Article Text

References (52)

Massless sector of ${AdS}_{3}$ superstrings: A geometric interpretation