NLO friction in symmetry restoring phase transitions

Interactions between bubbles/domain walls and the surrounding medium are a topic of active research, particularly as they apply to friction effects on accelerated expansion during first-order phase transitions. In this paper, we analyze for the first time friction pressure on relativistic walls in phase transitions where gauge symmetry is restored, particularly motivated by the observation that this pressure can, in principle, be negative at leading order, since some particles lose mass by definition as they cross into the new phase. We find, however, that at NLO, the soft emission of vectors from a charged current leads to positive pressure scaling as the wall's Lorentz boost factor $\gamma_w$, similar to the case of gauge symmetry breaking. Contrary to the latter case, we find that the dominant contribution in single emission is safe from IR divergences and exhibits a much stronger dependence on the wall shape. Finally, we argue that in any phase transition, no multi-particle process on the wall can impart negative pressure greater than the leading order result, in the asymptotic limit of large velocity.