Massless sector of AdS_3 superstrings: a geometric interpretation

TL;DR

This paper explores the geometric interpretation of the q-deformed Poincare' supersymmetry in AdS_3/CFT_2 massless scattering, revealing how the S-matrix can be viewed as a path-ordered exponential of a flat connection, with implications for integrability.

Contribution

It introduces a geometric framework for understanding the boost invariance of the S-matrix in AdS_3/CFT_2 massless scattering, including a novel interpretation using covariant derivatives and flat connections.

Findings

S-matrix is invariant under boosts with a non-local coproduct.

The boost action can be expressed as a differential operator, leading to a geometric picture.

A simplified algebraic Bethe ansatz supports the proposed 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.