Massive dressing factors for mixed-flux AdS$_3$/CFT$_2$

TL;DR

This work constructs and tests massive dressing factors for the mixed-flux AdS3×S3×T4 string, fixing them via crossing, unitarity, and CP/parity constraints in both string and mirror kinematics. The authors formulate a κ-deformed BES factor together with a modified Hernandez-López component and an odd part, organizing the full dressing phase for mirror excitations and then analytically continuing to the string region, including bound-state fusion. They verify crossing and unitarity across kinematics, analyze perturbative limits at large tension and in the relativistic regime, and discuss possible CDD additions. The results provide a consistent framework for the mirror TBA of mixed-flux AdS3 strings and pave the way to incorporating massless modes and broader bound-state sectors, with important links to the dual CFTs and known RR-limit results.

Abstract

We follow up on our proposal for dressing factors for the mixed-flux $AdS_3\times S^3\times T^4$ background presented in arXiv:2402.11732. We discuss in detail the analytic properties of the dressing factors in the string and mirror kinematics for fundamental massive particles and bound states. We prove that the dressing factors are unitary and CP-invariant in the string kinematics, parity invariant in the mirror, and solve the crossing equations in both kinematics. In the limit of pure Ramond-Ramond flux they reduce to the known ones. Finally, we present their expansion at strong tension, as well as in the (small-RR-flux) relativistic limit, finding agreement with the literature.

Figures (10)

• Figure 1: Left panel: The branch point (solid dot) and cut (zigzag line) of $x_{{\text{L}}}(u)$ on the $u$-plane; The cut's edges (solid and dashed lines) are mapped to an unbounded curve in the $x$-plane (right panel).
• Figure 2: Left panel: The three branch points (solid dots) and cuts (zigzag line) of $x_{{\text{R}}}(u)$ on the $u$-plane. We call the cyan cut the "main" one. Its edges (solid and dashed cyan lines) are mapped to a bounded, open curve in the $x$-plane, while the edges of the other two cuts are mapped to the half-line in the $x$-plane (right panel). The images of the branch points are denoted by empty dots.
• Figure 3: Left: The two branch points (solid dots) and cuts (zigzag line) of ${\tilde{x}}_{{\text{L}}}(u)$ and ${\tilde{x}}_{{\text{R}}}(u)$ on the $u$-plane, respectively. We call the cyan cut the "main" one. Its edges (solid and dashed cyan lines) are mapped to the positive semi-axis in the $x$-plane, while the edges of the second cut are mapped to the lower edge of the $\ln x$ cut (right panels). The images of the branch points are denoted by empty dots.
• Figure 4: The asymptotic behaviour of $x_a(u)$ and ${\tilde{x}}_a(u)$ at large $|u|$ depends on the cut structure of the functions, as evidenced by the shading in different colours. The top-left and top-right panels depict the string variables and correspond to eq. \ref{['eq:xL_large_u']} and eq. \ref{['eq:xR_large_u']}, respectively. The bottom-left and bottom-right panels depict the mirror variables and correspond to eq. \ref{['eq:txL_large_u']} and \ref{['eq:txR_large_u']}, respectively.
• Figure 5: Left: the mirror region (shaded in green) with its boundary $\partial\mathcal{R}_-$. Right: the anti-mirror region (shaded in green) with its boundary $\partial\mathcal{R}_+$. Note that each boundary approaches $\tilde{x}_a=0$, where there is the branch point of the logarithm.