Correspondence ofZ2-orbifold string and torus string

We investigate the correspondence between a ${\mathrm{Z}}_2$ orbifold string and a torus string model which have the same vacuum amplitudes when they take particular radii. We show that ground states of the twisted sector of ${\mathrm{Z}}_2$ orbifold can be easily described by the torus string. In our formalism, we obtain the same amplitudes as those of Hamidi and Vafa, and of Dixon, Friedan, Martinec, and Shenker.