Characterization of loops with realizable generalized Dehn twists

Let $S$ be the surface under discussion, let $\gamma$ be an unoriented loop on $S$, and let $t_{\gamma}$ denote the generalized Dehn twist along $\gamma$. A loop is homotopic to a power of a simple closed curve if it is homotopic to $\delta^n$ for some simple closed curve $\delta$ and integer $n$. Characterization conjecture. If $t_{\gamma}$ is realizable as a diffeomorphism, then $\gamma$ is homotopic to a power of a simple closed curve. This conjecture proposes a characterization of the simple closed curves, up to taking powers, whose generalized Dehn twists can be realized by diffeomorphisms; the preceding results establish non-realizability for broad classes of non-simple loops, but do not settle the converse in general.