String melting in a photon bath

We compute the decay rate of a metastable cosmic string in contact with a thermal bath by finding the instanton solution. The new feature is that this decay rate is found in the context of non thermal scalar fields in contact with a thermal bath of photons. In general, to make topologically unstable strings stable, one can couple them to such a bath. The resulting plasma effect creates metastable configurations which can decay from the false vacuum to the true vacuum. In our specific set-up, the instanton computation is realized for the case of two out-of-equilibrium complex scalar fields : one is charged and coupled to the photon field, and the other is neutral. New effects coming from the thermal bath of photons make the radius of the nucleated bubble and most of the relevant physical quantities temperature-dependent. However, the temperature appears in a different way than in the purely thermal case, where all scalar fields are in thermal equilibrium. As a result of the tunneling, the core of the initial string melts while bubbles of true vacuum expand at the speed of light.