Weil pairing on twisted curves

We define and study the Weil pairing on the moduli of twisted curves. If $X$ is a twisted curve, then we can combinatorially describe a certain subgroup and a quotient group of $\text{Pic}(X)[2]$ that are Weil dual. Moreover, the pairing between them can be realized as combinatorial integration-homology pairing on the dual graph of $X$. We also prove that the kernel of the tropicalization is isotropic for the Weil pairing.