AdS3 integrability, Sine-Gordon and fractional supersymmetry

TL;DR

The work addresses the massless $S$-matrix in $AdS_3\times S^3\times T^4$ and its connections to Sine-Gordon at a special coupling, revealing a fractional supersymmetry underlying the scattering with particles obeying fractional statistics. By exploiting the coproduct of a quantum affine symmetry, the authors show how ${\cal N}=2$ structure emerges and construct interpolating S-matrices $S_\alpha$ and $S_{\alpha+}$ that smoothly connect massless $AdS_3$, Sine-Gordon, and mixed-flux relativistic scattering while remaining relativistically invariant and unitary in the braiding sense. Both families solve the Yang–Baxter equation and admit a fractional-statistics interpretation, suggesting a unified parent integrable system that encompasses the various relativistic corners of the AdS$_3$/CFT$_2$ landscape. The paper further generalizes to generic $q$ and employs Drinfeld twists to relate to mixed-flux cases, providing explicit dressing-phase structures and crossing relations. Overall, the results offer a cohesive framework for embedding AdS$_3$ massless and mixed-flux integrable structures into a single, fractional-supersymmetric scattering theory.

Abstract

The massless S-matrix of the pure RR AdS3 X S3 X T4 theory is very similar but not quite the same as Fendley-Intriligator's N=2 S-matrix, in turns related to Sine-Gordon taken at a special coupling. In this short note we review the reason why supersymmetry emerges but with a fractional statistics of the particles. We then use this to obtain a very simple interpolating S-matrix between massless AdS3 and Sine-Gordon, and further find two interpolating S-matrices between these and the mixed-flux relativistic S-matrix, solving the Yang-Baxter equation all the way in-between. They are all relativistic invariant and braiding unitary, can be written in terms of particles with fractional statistics, and they might serve the purpose to embed into a parent integrable system.