Dynamics of cosmic strings with higher-dimensional windings

TL;DR

This paper explores how higher-dimensional windings in cosmic strings can lead to tensionless configurations in four dimensions, affecting string dynamics and potentially resulting in static or special solutions.

Contribution

It introduces a new understanding of tensionless states in cosmic strings with higher-dimensional windings and derives explicit solutions for various configurations.

Findings

Higher-dimensional windings can render strings effectively tensionless in 4D.

Critical configurations occur when half the string length is in large dimensions and half in compact space.

Explicit solutions for straight, circular, and arbitrary configurations are provided.

Abstract

We consider F-strings with arbitrary configurations in the Minkowski directions of a higher-dimensional spacetime, which also wrap and spin around $S^1$ subcycles of constant radius in an arbitrary internal manifold, and determine the relation between the higher-dimensional and the effective four-dimensional quantities that govern the string dynamics. We show that, for any such configuration, the motion of the windings in the compact space may render the string effectively tensionless from a four-dimensional perspective, so that it remains static with respect to the large dimensions. Such a critical configuration occurs when (locally) exactly half the square of the string length lies in the large dimensions and half lies in the compact space. The critical solution is then seen to arise as a special case, in which the wavelength of the windings is equal to their circumference. As examples, long straight strings and circular loops are considered in detail, and the solutions to the equations of motion that satisfy the tensionless condition are presented. These solutions are then generalized to planar loops and arbitrary three-dimensional configurations. Under the process of dimensional reduction, in which higher-dimensional motion is equivalent to an effective worldsheet current (giving rise to a conserved charge), this phenomenon may be seen as the analogue of the tensionless condition which arises for superconducting and chiral-current carrying cosmic strings.