 by means of the duality relation.  ### $U\left(  \varphi\right)  =\eta\varphi^{0}+\sigma\varphi^{0}$  The duality transformations given by Eqs. (\[phitanspol\]), (\[xtanspol\]), (\[Geta\]), and (\[kapsig\]) are $$\begin{aligned} \phi &  \rightarrow\varphi^{-0},\