Space-Time Symmetries, T-Duality and Gauge Theory

In this paper we study U(1) gauge transformations on the space-time coordinates and on the background fields $g_{\mu\nu}$ and $\phi$. For some special gauge functions, gauged coordinates and gauged U(1) field are equivalent to the rotated coordinates and rotated gauge field. We find gauge transformations that are symmetries of the string action. Also we obtain general $T$-duality transformations for the background fields. For special background fields this duality is equivalent to a gauge transformation.