Dynamics of self-interacting strings and energy-momentum conservation

TL;DR

This paper develops a finite, self-consistent dynamics for classical superstring models with self-interactions by enforcing local energy-momentum conservation, addressing ultraviolet divergences and extending non-renormalization insights.

Contribution

It introduces a fundamental principle based on energy-momentum conservation to derive finite equations of motion for self-interacting strings, overcoming divergence issues.

Findings

Ultraviolet divergences cancel out in uniform motion cases.

The derived dynamics are unique under the proposed principle.

The approach parallels superstring non-renormalization theorems.

Abstract

Classical strings coupled to a metric, a dilaton and an axion, as conceived by superstring theory, suffer from ultraviolet divergences due to self-interactions. Consequently, as in the case of radiating charged particles, the corresponding effective string dynamics can not be 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-defined distribution-valued energy-momentum tensor. Its continuity equation 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.