Supersymmetric Form of the String Action in the Presence of the Gauge Field

Abstract

In this manuscript 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 "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 are also obtained.