New Dressing Factors for AdS3/CFT2

TL;DR

This paper refines the AdS3/CFT2 worldsheet S matrix by introducing a new, crossing-consistent set of five dressing factors for AdS3xS3xT4. By stripping the BES factor and formulating rapidity-difference equations on the Beisert-type rapidity variables, the authors achieve a solution that preserves parity, braiding unitarity, and physical unitarity, while maintaining well-behaved analytic properties in both string and mirror regions and under bound-state fusion. The construction combines the BES phase with a Sine-Gordon-like auxiliary function and a monodromy factor, controlled by an auxiliary a(γ) function, to satisfy all crossing relations in massive, mixed, and massless sectors; it also matches known perturbative data at tree level and clarifies discrepancies in one-loop results through careful consideration of regularization and path choices. The framework yields explicit, fusion-friendly building blocks and enables explicit Bethe-Yang equations, providing a robust path to the finite-volume spectrum and potential extensions to mixed-flux backgrounds. Overall, the work resolves prior inconsistencies, clarifies the analytic structure of massless dressings, and offers a concrete, testable route toward a complete, finite-coupling spectrum for AdS3/CFT2 systems.

Abstract

The worldsheet S matrix of strings on the $AdS_3\times S^3\times T^4$ background is almost entirely fixed by symmetries, up to five functions -- the dressing factors. These must satisfy several consistency conditions, in particular a set of crossing equations. We find that the existing proposal for the dressing factors, while crossing invariant, violates some of these consistency conditions. We put forward a new set of dressing factors and discuss in detail their analytic properties in the string and mirror region, as well as under bound-state fusion.

Figures (5)

• Figure 1: The physical string region. In the leftmost panel, the physical string region for $x^+$ is $|x^+|>1$; in the middle panel, for $x^-$ is $|x^-|>1$; in the rightmost panel, we draw it for the $\gamma^+$ and $\gamma^-$ panel, where it takes the form of the strips between $-i\pi$ and $0$, and between $0$ and $+i\pi$, respectively.
• Figure 2: The mirror region. In the leftmost panel, the mirror region for $x^+$ is $\mathfrak{I}[x^+]<0$; in the middle panel, for $x^-$ is $\mathfrak{I}[x^-]<0$; in the rightmost panel, we draw it for the $\gamma^+$ and $\gamma^-$ panel, where it takes the form of the strips between $-\tfrac{3}{2}i\pi$ and $-\tfrac{1}{2}i\pi$, and between $-\tfrac{1}{2}i\pi$ and $+\tfrac{1}{2}i\pi$, respectively.
• Figure 3: The string, mirror and anti-string region in the massless kinematics. In all three cases, the "region" is actually a line, corresponding to real momentum particles. We denote the string region by a solid green line (upper-half-circle in the $x$-plane), the mirror region by a dashed purple line (real segment in the $x$-plane), and the anti-string region by a solid orange line (lower-half-circle in the $x$-plane).
• Figure 4: The $u$ plane. In the left panel, the function $\gamma^+(u)$ has branch points at $u=\pm 2-\tfrac{i}{h}$ and the branch cut runs on the red wavy line; the function $\gamma^-(u)$ has branch points at $u=\pm 2+\tfrac{i}{h}$ and the branch cut runs on the blue wavy line. In the right panel, we make a similar drawing for $\tilde{\gamma}^\pm(u)$; this time the branch cuts are "long", i.e. they go to infinity.
• Figure 5: The $u$ plane for massless particles. In the left panel, the function $\gamma(u)$ has branch points at $u=\pm 2$ and the branch cut runs on the green wavy line; real momentum and positive energy corresponds to $\gamma(u)$ just above the cut. In the right panel, we make a similar drawing for $\tilde{\gamma}(u)$; this time the branch cuts are "long", i.e. they go to infinity, and real values of the mirror momentum as well as positive values of the mirror energy correspond to $\tilde{\gamma}(u)$ just above the cut.