http://arxiv.org/abs/1707.09967
We discuss the non-conservation of fermion number (or chirality breaking, depending on the fermionic charge assignment) in Abelian gauge theories at finite temperature. We study different mechanisms of fermionic charge disappearance in the high temperature plasma, with the use of both analytical estimates and real-time classical numerical simulations. We investigate the random walk of the Chern-Simons number $N_{\rm CS} \propto \int d^4x F_{\mu\nu}{\tilde F}^{\mu\nu}$, and show that it has a diffusive behaviour in the presence of an external magnetic field $B$. This indicates that the mechanism for fermionic number non-conservation for $B \neq 0$, is due to fluctuations of the gauge fields, similarly as in the case of non-Abelian gauge theories. We determine numerically the rate of chirality non-conservation associated with this diffusion, finding it larger by a factor $\sim 60$ compared to previous theoretical estimates. We also perform numerical simulations for the system which contains a chemical potential $\mu$ representing a fermionic charge density, again both with and without an external magnetic field. When $B=0$, we observe clearly the expected instability of the system for $\mu \neq 0$, as long as the chemical potential exceeds a critical value $\mu > \mu_c(L)$, which depends on the size $L$ of the system. When $B \neq 0$, the fluctuations of bosonic fields lead to the transfer of chemical potential into Chern-Simons number for arbitrary $\mu$.
D. Figueroa and M. Shaposhnikov
Tue, 1 Aug 17
55/55
Comments: 60 pages, 20 figures
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