A dynamic su(1|1)^2 S-matrix for AdS3/CFT2

TL;DR

This paper derives the all-loop two-body S-matrix for the AdS3/CFT2 massive sector from the centrally extended su(1|1)^2 symmetry of the d(2,1;α)^2 spin-chain. By carefully constructing left/right-moving representations and two central extensions, the authors obtain a highly constrained matrix structure that satisfies unitarity, LR-symmetry, and the Yang-Baxter equation, while leaving four antisymmetric scalar factors to be fixed by crossing relations. The formalism reveals nontrivial scattering between different-mass excitations and connects to the psu(2|2) framework, highlighting both consistency with known integrated structures and novel mass-mixing dynamics. Open directions include incorporating massless modes, refining the crossing equations, and exploring bound-state sectors and non-asymptotic spectra via the thermodynamic Bethe ansatz.

Abstract

We derive the S-matrix for the d(2,1;alpha)^2 symmetric spin-chain of AdS3/CFT2 by considering the centrally extended su(1|1)^2 algebra acting on the spin-chain excitations. The S-matrix is determined uniquely up to four scalar factors, which are further constrained by a set of crossing relations. The resulting scattering includes non-trivial processes between magnons of different masses that were previously overlooked.

Figures (4)

• Figure 1: Two Dynkin diagrams for $\mathfrak{d}(2,1;\alpha)$. Diagram \ref{['fig:dynkin-d21a-orig']} corresponds to the choice of positive roots in \ref{['eq:d21a-pos-roots-I']}, while diagram \ref{['fig:dynkin-d21a-dual']} corresponds to the choice in \ref{['eq:d21a-pos-roots-II']}.
• Figure 2: Unitarity. Acting twice with the S-matrix $\mathcal{S}$ on a two-particle state gives back the original state.
• Figure 3: The Yang-Baxter equation relates the two different ways of scattering three particles to each other.
• Figure 4: The scattering of a fundamental excitation with a singlet is trivial.