Impact of Dynamical Tensions in Modified String and Brane Theories
  First we briefly outline the general construction of Dp-brane models with dynamical tensions. We then proceed to a more detailed discussion of a modified string model where the string tension is related to the potential of (an external) world-sheet electric current. We show that cancellation of the pertinent conformal anomaly on the quantum level requires the dynamical string tension to be a square of a free massless world-sheet scalar field. 
E.I. Guendelman, A. Kaganovich, E. Nissimov and S. Pacheva