25678 2410.19906 10.1007/JHEP03(2025)022 22 22 Chern-Simons induced thermal friction on axion domain walls 02 Physical Sciences 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics Regular Article - Theoretical Physics 1 55 2025 3 5 2024 11 12 2025 2 6 2025 3 5 The Author(s) 2025 Open Access. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. 13130 2025 2025 3 3 Saquib Hassan saquib.hassan@chch.ox.ac.uk Gaurang Ramakant Kane gaurang.kane@physics.ox.ac.uk John March-Russell john.march-russell@physics.ox.ac.uk Georges Obied georges.obied@physics.ox.ac.uk https://ror.org/052gg0110 grid.4991.5 0000 0004 1936 8948 Rudolf Peierls Centre for Theoretical Physics University of Oxford Parks Road Oxford OX1 3PU United Kingdom https://ror.org/052gg0110 grid.4991.5 0000 0004 1936 8948 Christ Church College University of Oxford St Aldate’s Oxford OX1 1DP United Kingdom Abstract We study the dynamics and interactions of the solitonic domain walls that occur in realistic axion electrodynamics models including the Chern-Simons interaction, aϵ μνλσ F μν F λσ , between an axion a(x) of mass m a , and a massless U(1) gauge field, e.g. EM, interacting with strength α = e 2/4π with charged matter, e.g. electron-positron pairs. In particular, in the presence of a U(1) gauge-and-matter relativistic thermal plasma we study the friction experienced by the walls due to the Chern-Simons term. Utilizing the linear response method we include the collective effects of the plasma, as opposed to purely particle scattering across the wall (as is done in previous treatments) which is valid only in the thin wall regime that is rarely applicable in realistic cases. We show that the friction depends on the Lorentz-γ-factor-dependent inverse thickness of the wall in the plasma frame, ℓ −1 ~ γm a , compared to the three different plasma scales, the temperature T, the Debye mass m D ~ α T $$ \sqrt{\alpha }T $$ , and the damping rate Γ ~ α 2 T, and elucidate the underlying physical intuition for this behavior. (For friction in the thin-wall-limit we correct previous expressions in the literature.) We further consider the effects of long-range coherent magnetic fields that are possibly present in the early universe and compare their effect with that of thermal magnetic fields. We comment on the changes to our results that likely apply in the thermal deconfined phase of a non-Abelian gauge theory. Finally, we briefly discuss the possible early universe consequences of our results for domain wall motion and network decay, stochastic gravitational wave production from domain wall networks, and possible primordial black hole production from domain wall collapse, though a more complete discussion of these topics is reserved for a companion paper. Keywords Axions and ALPs Early Universe Particle Physics Thermal Field Theory ArXiv ePrint: 2410.19906