Global String Radiation

We study Goldstone boson (or axion) radiation from global $U(1)$-strings making direct quantitative comparisons between numerical scalar field theory simulations and linearized analytic calculations in the dual antisymmetric tensor representation. Concentrating on periodic long string configurations, we show excellent correspondence for both the amplitude and spectrum of radiation. We also find good agreement with a linearized analytic model for radiation backreaction, demonstrating that damping due to the lowest n=2 harmonic is effective in strongly suppressing higher harmonics. This work establishes the validity of the Kalb-Ramond action in describing low-energy global string dynamics, along with the associated self-field renormalization of the equations of motion. We also describe the different nature of massive radiation from high curvature regions and the collapse and annihilation of a circular loop. As an application in axion models, we discuss the relative loop and long string radiation contribution to a cosmological bound on the axion mass. A parallel linearized formalism for gravitational radiation is also provided.