Dressing Factors for Mixed-Flux $AdS_3\times S^3\times T^4$ Superstrings

TL;DR

The paper constructs a consistent, minimal solution for the dressing factors of mixed-flux AdS3xS3xT4 strings in both mirror and string kinematics by combining κ-deformed BES and HL contributions with an odd component. The approach satisfies crossing, unitarity, and fusion constraints and aligns with perturbative and semiclassical results, including large-tension and near-BMN expansions, as well as a relativistic limit. These dressing factors are essential for obtaining the exact spectrum via mirror TBA and advance the understanding of integrability in mixed-flux backgrounds, with promising directions toward massless sectors and dual CFT connections.

Abstract

We propose the dressing factors for the scattering of massive particles on the worldsheet of mixed-flux $AdS_3\times S^3\times T^4$ superstrings, in the string and mirror kinematics. The proposal passes all self-consistency checks in the both kinematics, including for bound states. It matches with perturbative and semiclassical computations from the string sigma model, and with its relativistic limit.

Figures (2)

• Figure 1: Analytic structure of $x_{{\text{L}},{\text{R}}}(u)$. Top left: $x_{{\text{L}}}(u)$ has a single branch cut (zigzag line). The images of its edges give an unbounded curve in the $x_{{\text{L}}}$-plane (top right). Bottom left: $x_{{\text{R}}}(u)$ has two more branch cuts (magenta and orange). Their images are straight lines in the $x_{{\text{R}}}$ plane, just above/below the cut of $\ln x$ (bottom right). The cyan curves split each $x_{{\text{L}},{\text{R}}}$ planes in two parts, the one including $x_{{\text{L}},{\text{R}}}=+\infty$ is the physical region, or "string" region; The one inside is the "antistring" region, where antiparticles live.
• Figure 2: Analytic structure of $\tilde{x}_{{\text{L}},{\text{R}}}(u)$. Left top/bottom: each of $\tilde{x}_{{\text{L}}}(u)$ and $\tilde{x}_{{\text{R}}}(u)$ has two branch cuts; exchanging $L\leftrightarrow R$ is a reflection about the real-$u$ line. Right top/bottom: the images of the $u$-plane cuts are straight lines on the $\tilde{x}_{{\text{L}},{\text{R}}}$ plane; For $\tilde{x}<0$ they run just below the cut of $\ln\tilde{x}$. Sending $\kappa\to0$ one immediately recovers the familiar structure of the pure-RR mirror theory Frolov:2021bwp. The lower-half $\tilde{x}_{{\text{L}},{\text{R}}}$-plane is the physical region for mirror particles ("mirror" region), and the upper half-plane for antiparticles ("antimirror" region).