The non-relativistic rapidity substitution conjecture for massless AdS/CFT R-matrices

Let $p$ be the momentum of a massless mode and define the non-relativistic rapidity

$$\gamma \equiv \log \tan \frac{p}{4}.$$

For relativistic massless scattering, let $\theta$ denote the rapidity difference, and let right-right and left-left modes refer to scattering states of the corresponding chiralities. Non-relativistic rapidity substitution conjecture. In AdS/CFT, every massless non-relativistic R-matrix governing the scattering of right-right or left-left modes is obtained from the massless relativistic one by the substitution

$$\theta \longrightarrow \gamma.$$

Equivalently, for two particles one replaces $\theta=\theta_1-\theta_2$ by $\gamma=\gamma_1-\gamma_2$, with

$$\gamma=\log \tan \frac{p_1}{4}-\log \tan \frac{p_2}{4}.$$

The conjecture expresses a simple relation between relativistic and non-relativistic massless scattering matrices and is supported in the examples discussed, including undeformed $AdS_2\times S^2\times T^6$ and $AdS_3\times S^3\times T^4$, but its extension to more general AdS/CFT backgrounds remains to be established.