Chiral charge dynamics in Abelian gauge theories at finite temperature

Abstract

Abstract We study fermion number non-conservation (or chirality breaking) in Abelian gauge theories at finite temperature. We consider the presence of a chemical potential μ for the fermionic charge, and monitor its evolution with real-time classical lattice simula- tions. This method accounts for short-scale fluctuations not included in the usual effective magneto-hydrodynamics (MHD) treatment. We observe a self-similar decay of the chemi- cal potential, accompanied by an inverse cascade process in the gauge field that leads to a production of long-range helical magnetic fields. We also study the chiral charge dynamics in the presence of an external magnetic field B, and extract its decay rate $$ {\varGamma}_5\equiv \frac{d\ \log\ \mu }{dt} $$ Γ 5 ≡ d log μ dt . We provide in this way a new determination of the gauge coupling and magnetic field de- pendence of the chiral rate, which exhibits a best fit scaling as $$ {\varGamma}_5{\propto}^{\raisebox{1ex}{$11$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{B}^2 $$ Γ 5 ∝ 11 2 B 2 . We confirm numerically the fluctuation-dissipation relation between Γ5 and Γdiff , the Chern-Simons diffusion rate, which was obtained in a previous study. Remarkably, even though we are outside the MHD range of validity, the dynamics observed are in qualitative agreement with MHD predictions. The magnitude of the chiral/diffusion rate is however a factor ∼ 10 times larger than expected in MHD, signaling that we are in reality exploring a dif- ferent regime accounting for short scale fluctuations. This discrepancy calls for a revision of the implications of fermion number and chirality non-conservation in finite tempera- ture Abelian gauge theories, though no definite conclusion can be made at this point until hard-thermal-loops are included in the lattice simulations.