Fermionic current-carrying cosmic strings: zero-temperature limit and equation of state

The equation of state for a superconducting cosmic string whose current is due to fermionic zero modes is derived analytically in the case where the back-reaction of the fermions to the background is neglected. It is first shown that the zero mode fermions follow a zero temperature distribution because of their interactions (or lack thereof) with the string-forming Higgs and gauge fields. It is then found that the energy per unit length U and the tension T are related to the background string mass m through the simple relation U+T=2m*m. Cosmological consequences are briefly discussed.