On mixed-flux worldsheet scattering in AdS3/CFT2

TL;DR

The paper develops a complete bootstrap for the worldsheet S matrix of mixed-flux AdS_3×S^3×T^4 strings by exploiting a relativistic limit that fixes all dressing factors. It constructs the particle spectrum and bound-state representations, derives crossing equations across massive and massless sectors, and provides explicit relativistic S-matrices and minimal dressing factors (including CDD contributions) consistent with unitarity and fusion. The results reveal a tower of bound states tied to the WZNW level k, identify two massless multiplets, and connect to Toda-type S-matrix structures, offering a robust testbed for the full mixed-flux dressing program and insights into low NSNS flux regimes. This relativistic framework serves as a crucial check for proposed dressings in the nonrelativistic theory and informs future TBA/mirror analyses of the complete model.

Abstract

Strings on AdS3xS3xT4 with mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz flux are known to be classically integrable. This is a crucial property of this model, which cannot be studied by conventional worldsheet-CFT techniques. Integrability should carry over to the quantum level, and the worldsheet S matrix in the lightcone gauge is known up to the so-called dressing factors. In this work we study the kinematics of mixed-flux theories and consider a relativistic limit of the S matrix whereby we can complete the bootstrap program, including the dressing factors for fundamental particles and bound states. This provides an important test for the dressing factors of the full worldsheet model, and offers new insights on the features of the model when the amount of NSNS flux is low.

Figures (6)

• Figure 1: The physical region of the $x$-plane (on the right) and associated one-cut $u$-plane (on the left) for $\kappa>0$. The shaded regions are removed from the $x$-plane. The different colours show how the $u$-plane on the left is mapped to the corresponding $x$-plane on the right. The zigzag line in the $u$-plane corresponds to a cut. By crossing this cut we end up in the $u$-plane shown in figure \ref{['antistring_u_x_planes_positive_k']}, which is mapped to the antistring region of the $x$-plane.
• Figure 2: The antistring or crossed region in the $x$-plane region (on the right) and associated three-cut $u$-plane (on the left) for $\kappa>0$. As in the previous figure, the shaded regions are removed from the $x$-plane and the different colours show the map between the $u$ and $x$ plane. By crossing the cut $(-\infty, u_+)$ in the $u$-plane we return to the $u$-plane depicted in figure \ref{['string_u_x_planes_positive_k']}. Similar conventions are used to show the map between $u$ and $x$ planes in figures \ref{['string_u_x_planes_negative_k']} and \ref{['antistring_u_x_planes_negative_k']}.
• Figure 3: The physical region of the $x$-plane (on the right) and associated three-cut $u$-plane (on the left) for $\kappa<0$. Notice that the number of cuts in the $u$-plane are different when $\kappa<0$ with respect to $\kappa>0$.
• Figure 4: The antistring region of the $x$-plane (on the right) and associated one-cut $u$-plane (on the left) for $\kappa<0$.
• Figure 5: Behaviour of $E^2$ at different values of $h$ for $m$ and $k$ fixed. For $\frac{k}{h} \sim 1$ there are many local minima, as shown in figure \ref{['fig:three_dispersion_relations_1']}, while increasing $\frac{k}{h}$ these minima disappear (see figures \ref{['fig:three_dispersion_relations_2']} and \ref{['fig:three_dispersion_relations_3']}) and one global minimum remains.