On curvature corrections for field theory cosmic strings

TL;DR

This paper derives and validates an effective action for field theory cosmic strings, revealing the role of massive modes and confirming predictions through lattice simulations, including the instability of excited strings.

Contribution

It provides a systematic derivation of the low energy effective action for cosmic strings, including curvature corrections from massive modes, validated by numerical simulations.

Findings

Curvature corrections are absent for Goldstone modes alone.

Massive modes couple to the worldsheet Ricci scalar, influencing curvature effects.

Excited strings exhibit a parametric instability transferring energy to Goldstone modes.

Abstract

We present a combined analytical and numerical study of the effective action of field theory cosmic strings in the Abelian-Higgs model in flat space. Starting directly from the underlying solitonic field theory description, we provide a systematic derivation of the low energy effective action and present evidence for the absence of nontrivial curvature correction terms when only the translational Goldstone modes are retained. Using this framework, we extend the effective theory to include higher energy fluctuations of the soliton profile, which map to massive degrees of freedom propagating on the worldsheet. We show that the leading curvature contribution enters only through the coupling between these massive modes and the worldsheet Ricci scalar. We validate the resulting effective theory via lattice simulations of the full field theory equations of motion in flat space, implemented with Adaptive Mesh Refinement to capture the string dynamics across different scales. The numerical simulations confirm the dynamics obtained using the effective action in its validity range. Furthermore, they also demonstrate the existence of the predicted parametric instability of excited strings that drives the transfer of energy from massive excitations to the Goldstone sector.