Testing Nambu-Goto approximation of cosmic string by lattice field simulations

The precise calculation of gravitational wave (GW) and particle emissions from cosmic string networks is of significant theoretical and experimental interest. In this Letter, we perform numerical simulations of near-global and local string networks, comparing the GW spectra predictions from both lattice field simulation and the Nambu-Goto (NG) approximation methods. We find the discrepancy between the GW spectra computed via the NG approximation and the lattice field simulation is negligible for near-global string and grow with increasing gauge coupling. Additionally, we confirm that particle emission significantly dominates energy emission, with the ratio of GW energy to particle energy approximately $10^{-3}$ to $10^{-2}$ for both near-global and local string scenarios.