Kaluza-Klein origin for the superstring tension

The natural configuration space of a string in a background antisymmetric tensor potential is not loop space but a principal U(1) bundle over loop space. This allows a Kaluza-Klein-like interpretation of the string tension as momentum along the U(1) fiber, and a similar interpretation is possible for a $p$-dimensional object. The "higher-dimensional" action incorporating this momentum as a dynamical variable is given for a $p$-dimensional supersymmetric extended object, in a general supergravity background. Its relevance, for a flat background, to "classical anomalies" in the supersymmetry algebra is explained.