Superstring in the Presence of the Worldsheet Gauge Field

We study the superstring theory with an Abelian worldsheet gauge field. The components of the gauge field appear as a space and a time coordinates. We call them as “fictitious coordinates”. The worldsheet supersymmetry and the Poincar'e symmetry of this model will be analyzed. The $T$-duality and quantization of the two fictitious coordinates also will be obtained.