On the Dressing Factors, Bethe Equations and Yangian Symmetry of Strings on AdS3 x S3 x T4

TL;DR

This work completes a coherent integrable picture for strings on AdS3×S3×T4 by resolving the massless sector: it constructs minimal, crossing-consistent dressing factors for massless and mixed-mass scattering, derives all-loop Bethe equations including massless modes, and establishes a Yangian symmetry for the massless S-matrix. It shows how massless excitations fit into the same algebraic framework as massive ones, including evaluation representations and crossing, and investigates their near-BMN limit with comparisons to perturbative results. The analysis clarifies the absence of massless bound states and reveals detailed degeneracies tied to the underlying psu(1,1|2)^2 symmetry and torus translations. These results advance the exact spectral problem for AdS3/CFT2, providing a foundation for finite-size corrections and future integrability tools such as a quantum spectral curve in the massless sector.

Abstract

Integrability is believed to underlie the AdS3/CFT2 correspondence with sixteen supercharges. We elucidate the role of massless modes within this integrable framework. Firstly, we find the dressing factors that enter the massless and mixed-mass worldsheet S matrix. Secondly, we derive a set of all-loop Bethe Equations for the closed strings, determine their symmetries and weak-coupling limit. Thirdly, we investigate the underlying Yangian symmetry in the massless sector and show that it fits into the general framework of Yangian integrability. In addition, we compare our S matrix in the near-relativistic limit with recent perturbative worldsheet calculations of Sundin and Wulff.

Figures (12)

• Figure 1: The crossing transformation for massive variables in the $x^\pm$ planes. Note that, following the conventions of Borsato:2013hoa, the path $\gamma$ crosses the unit circle below the real line. The red and blue zig-zag patterns depict the branch cuts of the massive dressing factors Borsato:2013hoa.
• Figure 2: The $p$- and $x$-planes for massless particles. The thick magenta line indicates the domain of real physical momenta. The zig-zag patterns denote where the energy changes sign. Given a point $p_0$ or $x_0$ in corresponding to the real momentum, we depict curves $\gamma_1,\gamma_2$ for the crossing transformation. On the $p$-plane, these send $p_0\to-p_0$ and cross a cut of the energy. On the $x$-plane, we have $x_0\to 1/x_0$ while crossing the real line with $|x|>1$.
• Figure 3: The $u$-plane for massless variable.
• Figure 4: Red dashed lines correspond to the branch cuts of the integrand, while red dots to the poles. In this specific example we move the contour of integration (blue line) from the upper semicircle to the real interval $[-1,+1]$ and we pick up a pole.
• Figure 5: The Left and Right massive modules. We indicate explicitly only the lowering supercharges, corresponding to the arrows pointing downwards. In each module the fermions transform in a doublet of $\mathfrak{su}(2)_\bullet$.