Normalized ground states for a fractional Choquard system in $\mathbb{R}$

In this paper, we study the following fractional Choquard system \begin{align*} \begin{split} \left{ \begin{array}{ll} (-Δ)^{1/2}u=λ_1 u+(I_μF(u,v))F_u (u,v), \quad\mbox{in}\ \ $\mathbb{R}$, (-Δ)^{1/2}v=λ_2 v+(I_μF(u,v)) F_v(u,v), \quad\mbox{in}\ \ $\mathbb{R}$, \displaystyle\int_{$\mathbb{R}$}|u|^2$\mathrm{d}$x=a^2,\quad \displaystyle\int_{$\mathbb{R}$}|v|^2$\mathrm{d}$x=b^2,\quad u,v\in H^{1/2}($\mathbb{R}$), \end{array} \right. \end{split} \end{align*} where $(-\mathrm{\Delta }{)}^{1\mathrm{/}2}$ denotes the $1\mathrm{/}2$-Laplacian operator, $a,b>0$ are prescribed, ${\lambda }_1,{\lambda }_2\in \mathbb{R}$, $I_{\mu }(x)=\frac{1}{\mathrm{\mid }x{\mathrm{\mid }}^{\mu }}$ with $\mu \in (0,1)$, $F_u,F_v$ are partial derivatives of $F$ and $F_u,F_v$ have exponential critical growth in $\mathbb{R}$. By using a minimax principle and analyzing the monotonicity of the ground state energy with respect to the prescribed masses, we obtain at least one normalized ground state solution for the above system.