Ricci-flow conjecture for the trigonometric deformation of the flag-variety sigma model

Let $G$ be a compact group with complexification $G_{\mathbb C}$, let $B$ be a Borel subgroup, and let $s$ be the trigonometric deformation parameter. The resulting family of metrics on the flag variety $G_{\mathbb C}/B$ has the maximal torus $T$ as an isometry group. After an $s$-dependent change of coordinates and setting $t=\log s$, Ricci-flow conjecture. the trigonometric integrable deformation of the sigma model should agree with the renormalization-group flow, and the family of metrics on $G_{\mathbb C}/B$ should satisfy the Ricci-flow equation. This identifies the integrable deformation with the renormalization-group evolution, but the source leaves proving or disproving the claim as an open question.