Anomalous non-conservation of fermion/chiral number in Abelian gauge theories at finite temperature

  • Daniel G. Figueroa
  • Mikhail Shaposhnikov
Open Access
Regular Article - Theoretical Physics


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, using both analytical estimates and real-time classical lattice numerical simulations. We investigate the random walk of the Chern-Simons number \( Q\propto {{\displaystyle \int d}}^4x{F}_{\mu \nu }{\tilde{F}}^{\mu \nu } \), 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 ≠ 0, is due to fluctuations of the gauge fields, similarly as in the case of non-Abelian gauge theories. We have determined numerically, with lattice simulations, the rate Γ of chirality non-conservation, extracting it from the diffusion process. We find that it is a factor ∼ 60 larger compared to previous theoretical estimates, what calls for a revision of the implications of Abelian fermion number and chirality non-conservation for baryogenesis, magnetogenesis and chiral symmetry evolution.


Anomalies in Field and String Theories Cosmology of Theories beyond the SM Lattice Quantum Field Theory Thermal Field Theory 


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.


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© The Author(s) 2018

Authors and Affiliations

  1. 1.Theory DepartmentCERNGeneve 23Switzerland
  2. 2.Institute of Physics, Laboratory of Particle Physics and Cosmology, École Polytechnique Fédérale de LausanneLausanneSwitzerland

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