On the $AdS_3\times S^3\times S^3\times S^1$ dressing factors

TL;DR

This work advances the integrability bootstrap for strings on AdS$_3\times$S$^3\times$S$^3\times$S$^1$ with mixed RR/NSNS flux by constructing dressing factors for massive worldsheet excitations in both string and mirror kinematics. The authors present explicit factorized S-matrix elements for same-mass and different-mass scattering, incorporating BES/HL-type phases where applicable and introducing homogeneous factors to satisfy crossing and braiding unitarity; they also analyze bound-state spectra and Bethe-string configurations in the mirror theory. The proposal matches available perturbative data across the parameter $\alpha$ that encodes the radii of the two three-spheres and remains consistent with the expected pole/zero structure, including giant-magnon related poles in string kinematics and mixed-mass mirror poles. The paper discusses the relation to quantum spectral curve approaches, addresses potential ambiguities in fusion (the so-called strange strings), and outlines future directions, including extension to massless modes and deeper QSC connections. Overall, this work provides a concrete, cross-checked S-matrix dressing framework for a rich AdS$_3$ background, enabling subsequent TBA/QSC analyses and advancing the holographic understanding of mixed-flux string theory.

Abstract

We propose dressing factors for massive excitations of the worldsheet S matrix of $AdS_3\times S^3\times S^3\times S^1$ supported by mixed Ramond--Ramond and Neveu-Schwarz--Neveu-Schwarz flux, in the "string" and "mirror" kinematics. Our proposal is compatible with crossing and unitarity, and it reproduces the available perturbative results for any ratio of the two three-spheres' radii.