A Teichmüller disk is an isometric holomorphic embedding of the hyperbolic plane into the Teichmüller space $T_{g,n}$. Let $QT_{g,n}$ be the bundle of quadratic differentials over $T_{g,n}$ whose fiber over a surface is the space of holomorphic quadratic differentials on it (with at worst simple poles at the marked points). The projection of the $GL(2,R)$ orbit of a quadratic differential $q$ in $QT_{g,n}$ is a Teichmüller disk $D_{q}$, and all Teichmüller disks arise this way. Here, we say that $q$ generates $D_{q}$. Half of a century ago, Earle posed the question of when is there a holomorphic retract of $T_{g,n}$ onto a given Teichmüller disk. Kra showed that a disk $D_{q}$ admits such a retract if $q$ has only even order zeros. In this talk, we will prove the converse of Kra’s theorem outside of very rare and explicit disks. This is joint work with Apisa, Lamel, Masanta, Novikov, Zimmer.