Chiral charge dynamics in Abelian gauge theories at finite temperature

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 simulations. 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 chemical 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 Γ 5 ≡ − d log µ dt . We provide in this way a new determination of the gauge coupling and magnetic field dependence of the chiral rate, which exhibits a best fit scaling as Γ 5 ∝ e 11/2 B 2 . We confirm numerically the fluctuation-dissipation relation between Γ 5 and Γ diff , 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 different regime accounting for short scale fluctuations. This discrepancy calls for a revision of the implications of fermion number and chirality non-conservation in finite temperature Abelian gauge theories, though not definite conclusion can be made at this point until hard-thermal-loops (HTL) are included in the lattice simulations.

Electrical conductivity of hot Abelian plasma with scalar charge carriers

“…The theoretical prediction for this rate can be derived in the framework of magnetohydrodynamics and the result is expressed in terms of electrical conductivity of the medium. Using our results for the conductivity in hot scalar QED, one would obtain the rate of chirality breaking which is roughly 10 times smaller than the numerical result of the simulations [15]. The explanation of this discrepancy may shed light on the mechanism of the chirality nonconservation in this system and the role of the scalar long-wavelength modes in this process.…”

“…The simulations conducted in Refs. [13][14][15] were aimed at calculating the rate of the chirality nonconservation in the external magnetic field in Abelian gauge theory with a scalar field. The theoretical prediction for this rate can be derived in the framework of magnetohydrodynamics and the result is expressed in terms of electrical conductivity of the medium.…”

“…Substituting the kinetic function (15) into Eq. (7), we obtain the following simple analytic expression for the conductivity:…”

“…One of the well-known examples of the latter system is the weakly-coupled plasma which exists in the Universe on different stages of its evolution. Knowing the conductivity of such a plasma is important for different cosmological applications, such as describing the evolution of primordial magnetic fields [1][2][3][4][5][6], the processes of lepto-and baryogenesis [7][8][9][10][11], the evolution of chiral asymmetry [12][13][14][15] etc.…”

“…In particular, in Refs. [13][14][15] the fermion chirality nonconservation in Abelian gauge theory with a charged scalar field was studied. The theoretical prediction for the chirality breaking rate depends on the electrical conductivity in the system, and it has to be compared with the numerical result measured from lattice simulations.…”