  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.
