Let $X$ be a smooth complex algebraic variety and $L$ be an $n$-torsion line bundle on $X$, i.e., a line bundle $L$ such that $L^n=\mathcal{O}_X(B)$, where $B$ is a divisor $B$ on $X$. Such a bundle determines a branched cover $Y\to X$ branched over $B$. The converse is also true: any such cover determines a line bundle $L$ and a divisor $B$ such that $L^n=\mathcal{O}_X(B)$. My question is that what is the analogous statement for real algebraic varieties? Do there exist line bundles and divisors as above? I appreciate any reference.
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