String Tension and the Generation of the Conformal Anomaly

The origin of the string conformal anomaly is studied in detail. We use a reformulated string Lagrangian which allows to consider the string tension $T_{0}$ as a small perturbation. The expansion parameter is the worldsheet speed of light c, which is proportional to $T_{0}$ . We examine carefully the interplay between a null (tensionless) string and a tensionful string which includes orders $c^{2}$ and higher. The conformal algebra generated by the constraints is considered. At the quantum level the normal ordering provides a central charge proportional to $c^{2}$. Thus it is clear that quantum null strings respect conformal invariance and it is the string tension which generates the conformal anomaly.