Dressing Factors and Mirror Thermodynamic Bethe Ansatz for mixed-flux AdS3/CFT2

TL;DR

This work completes the S-matrix bootstrap for mixed RR/NSNS flux in AdS3 x S3 x T4 by deriving massless dressings and establishing their crossing, unitarity, and symmetry properties. It then proposes mirror TBA equations that encapsulate the finite-volume spectrum across all string tensions, paving the way for quantitative spectral computations and connections to a potential QSC formulation. The analysis highlights novel features of the massless sector, including semionic exchange and non-unitary mirror dynamics, and demonstrates consistency with near-BMN and pure-RR limits. Together, these results unify the mixed-flux AdS3/CFT2 integrability framework and set the stage for numerical and analytic explorations of the spectrum and holographic dual CFT data.

Abstract

We complete the derivation of the dressing factors for the $AdS_3\times S^3\times T^4$ S matrix with mixed Ramond--Ramond and Neveu-Schwarz-Neveu-Schwarz flux, in the "string" and "mirror" kinematics. Using these, we propose the mirror Thermodynamic Bethe Ansatz equations which describe the spectrum of the model at any string tension.

Figures (6)

• Figure 1: The analytic continuation from the mirror region to the positive-string-momentum region. In the left panel we depict the $u$-plane; the point $u+i0$ crosses the main cut from above, and then $u\pm i0$ ends up on the cut of the (string) $x_{{\text{L}}}(u)$ function. Correspondingly, in the ${\tilde{x}}$-plane (right panel), ${\tilde{x}}^{+0}$ crosses the interval $(0,\xi)$, and then ${\tilde{x}}^{\pm0}\to x_{{\text{L}}}^{\pm0}$ which are complex and conjugate. The gray contour on the ${\tilde{x}}$-plane is the image of the edges of the gray cut of $x_{{\text{L}}}(u)$ on the $u$-plane.
• Figure 2: The analytic continuation from the mirror region to the negative-string-momentum region. In the left panel we represent the $u$ plane with the cuts of ${\tilde{x}}$ in blue and magenta; we additionally depict an (orange) cut at $-i\kappa$, which is the cut of $x_{{\text{R}}}(u)$. In this case, $u+i0$ crosses the cut at $+i\kappa$ and it is mapped to a different $u$-plane, that of $x_{{\text{R}}}(u)$, and it is continued to a point where $u>-\nu$. In this process, $u-i0$ does not cut any cut. The same transformation is easier to visualise on the ${\tilde{x}}$-plane (right) where ${\tilde{x}}^{+0}$ crosses the cut between $(-1/\xi,0)$; then, ${\tilde{x}}^{\pm0}$ end up on complex and conjugate points on a curve which is the image of the horizontal gray lines by the map $1/x_{{\text{R}}}(u)$.
• Figure 3: Graphs of real and imaginary parts of mirror energy and momenta as functions of real $u$ rapidity for $m<k$. The real part of mirror momentum is bounded from below.
• Figure 4: Graphs of real and imaginary parts of mirror energy and momenta as functions of real $u$ rapidity for $m>k$. The real part of mirror momentum runs from $-\infty$ to $+\infty$.
• Figure 5: Left: The curve on the $u$-plane where left mirror momentum ${\widetilde{p}}_{\text{L}}$ is real. The curve where ${\widetilde{p}}_{\text{R}}$ is real is a reflection of this one about the real line. Right: The real ${\widetilde{p}}_{\text{L}}(r)={\widetilde{p}}_{\text{R}}(r)$ as a function of $r=\Re(u)$.