  We study string theory on the analytically continued $\beta$ deformed
background proposed in hep-th/0509036. This non-static model provides a
solvable conformal field theory which describes time-dependent twisted string
dynamics. With the mini-superspace approach, we examine disk one-point
correlators of D-branes and compute the winding string pair production rate. We
find that these results are consistent with the CFT computation.
