On curvature corrections for field theory cosmic strings

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.

Figures (8)

• Figure 1: Top: Scalar and vector radial profile for the critical vortex. Bottom: Scalar and vector part of the first bound state solution of the linearized perturbation equations for the critical vortex. The modes are normalized using the standard $L^2$ norm on the plane.
• Figure 2: Initial data for a loop with $R_0=100$. The white lines depict the 6 levels of adaptive mesh refinement, with each box containing $32^3$ number of grid points. We use reflective boundary conditions in $x$, $y$ and $z$.
• Figure 3: Comparison of the evolution of the radius of the circular string loop as a function of time, with $R_0=10$. The black solid line corresponds to numerical solution. The red dashed line corresponds to the NG solution, while the dotted blue includes the correction in Eqn. \ref{['eq:Anderson']}.
• Figure 4: Slice across $y=0$ showing the $x-z$ plane evolution as the loop with initial radius $R_0=100$ collapses.
• Figure 5: Deviation from the Nambu-Goto solution for a loop with initial radius $R_0=32$: predictions from our effective model compared with those of Anderson:1997ip and with the field theory simulation.