Real-Time Nucleation and Off-Equilibrium Effects in High-Temperature Quantum Field Theories

We study real-time nucleation in perturbative high-temperature quantum field theories. Specifically, we incorporate the evolution of thermally fluctuating plasma driven out of equilibrium by nucleation. This plasma forms the thermal bath for the nucleating bubbles, and its off-equilibrium dynamics backreact on the bubbles, modifying the nucleation rate. Utilizing kinetic Boltzmann descriptions for the plasma particles, we derive that the nucleation rate in high-temperature quantum field theories is described by Langer's rate formula with effects arising from the off-equilibrium plasma, unaccounted for in Linde's thermal rate. Importantly, we establish a connection to equilibrium computations of nucleation rates, particularly with the effective field theory approach, showing that they correctly capture the leading parts of the logarithm of the rate. We also show that the dominant modifications to the nucleation rate from a light bosonic quantum field arise from its corresponding long-wavelength classical modes, rather than the associated hard particles. This work provides a foundation for further studies of off-equilibrium effects in nucleation rates for realistic Standard Model extensions.