Negative Infrared Divergent Corrections to the Global String Tension

We show that at large distances from an infinitely long global U(1) string, low energy Goldstone Bosons contribute a spatially dependent term to the energy density which is non-integrable. Specifically, this term diverges with the same form as the classical field theory contribution to the string tension, except with negative sign. This suggests that a careful analysis of the infrared degrees of freedom around the global string ought to yield an effective theory of the solitary string whose tension is finite. There are implications for axion cosmology.