XXZ/Sine-Gordon equivalence, paramter correspondance; Luther point in XXZ?

It has been argued that isotropic XXZ model corresponds to
an SG theory which flows to $K=1$, $u=0$ fixed point.

AFM XXZ model should correspond to some SG theory with K>1, u>0, which is dual to a massive Thirring model. We know if $K=2$, the massive Thirring model is free. It is called Luther point. Above that value, there are bound states.

My question is which parameter of XXZ corresponds to SG theory at Luther point?
Moreover, is there exact correspondence between parameters of XXZ and SG theory?

The convention is from Luttinger Liquid theory, $K=frac{1}{beta^2}$. $beta$
is an usual convention of Sine-Gordon theory:

for example in Lukyanov,Zamolodchikov: Exact expectation values of local fields in quantum sine-Gordon model