NLO friction in symmetry restoring phase transitions

TL;DR

This paper investigates the friction pressure on relativistic walls during symmetry restoring phase transitions, revealing that at next-to-leading order, the pressure remains positive and depends strongly on wall shape, contrary to initial expectations.

Contribution

It provides the first analysis of NLO friction pressure in symmetry restoring phase transitions, showing positive pressure and detailed dependence on wall shape, with implications for phase transition dynamics.

Findings

NLO soft vector emission leads to positive pressure.

Pressure scales with the wall's Lorentz boost factor γ_w.

Multi-particle processes cannot produce negative pressure exceeding leading order.

Abstract

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.