  For a family of Jacobians of smooth pointed curves there is a notion of
tautological algebra. There is an action of $\mathfrak{sl}_2$ on this algebra.
We define and study a lifting of the Polishchuk operator, corresponding to
$f\in \mathfrak{sl}_2$, on an algebra consisting of punctured Riemann surfaces.
As an application we prove that a collection of tautological relations on
moduli of curves, discovered by Faber and Zagier, come from a class of
relations on the universal Jacobian.
