Renormalisation of gravitational self interaction for wiggly strings

TL;DR

This paper demonstrates that the divergent gravitational self-interaction of elastic strings can be renormalized through an action adjustment, with applications to models of wiggly cosmic strings and their microscopic origins.

Contribution

It provides a general renormalization formula for gravitational self-interaction in elastic strings, linking macroscopic models with microscopic Nambu-Goto type descriptions.

Findings

Divergent self-interactions can be absorbed via action renormalization.

The formula applies to transonic models with wiggles.

Connection established between macroscopic and microscopic string models.

Abstract

It is shown that for any elastic string model with energy density $U$ and tension $T$, the divergent contribution from gravitational self interaction can be allowed for by an action renormalisation proportional to $(U-T)^2$. This formula is applied to the important special case of a bare model of the transonic type (characterised by a constant value of the product $UT$) that represents the macroscopically averaged effect of shortwavelength wiggles on an underlying microscopic model of the Nambu-Goto type (characterised by $U=T$).