Dynamics of self-interacting strings and energy-momentum conservation

Classical strings coupled to a metric, a dilaton and an axion, asconceived by superstring theory, suffer from ultraviolet divergences due to self-interactions. Consequently, as in the case ofradiating charged particles, the corresponding effective string dynamics cannotbe derived from an action principle. We propose a fundamental principle to build this dynamics, based on local energy-momentum conservation in terms of a well-defineddistribution-valued energy-momentum tensor. Its continuityequation implies a finite equation of motion for self-interacting strings. The construction is carried out explicitly for strings in uniform motion in arbitrary space-time dimensions, where we establish cancelations of ultraviolet divergences which parallel superstring non-renormalization theorems. The uniqueness properties of the resulting dynamics are analyzed.